The restriction on the 7th-level Sor/Wiz spell greater teleport [conj] (Player's Handbook 293) is that

you must have at least a reliable description of the place to which you are teleporting (such as a detailed description from someone else or a particularly precise map). If you attempt to teleport with insufficient information (or with misleading information), you disappear and simply reappear in your original location.

Ask the DM if there exists reliable descriptions that can be acquired that allow the spell greater teleport to reach the destination you want. Are there folks you can interview? Books to read? Tavern tales to absorb? Paintings to study? Sculpture gardens to enjoy? If a way of getting that reliable description exists, do what you must and find the destination that way.

If reliable descriptions don't exist, try scouting the area using an acquaintance.

If there's a creature with which you're familiar in or near the area to which you want to teleport, target that creature with the spell sending [evoc] (PH 275-6) (which is an evocation spell with no saving throw and that doesn't allow spell resistance), explaining to the target who you are, that you'll be casting the spell scrying [div] (PH 274-5) on him in just a minute, and that the creature is to fail the saving throw. The creature can do that.

Cast the spell scrying on the creature and study the area around the creature. If you can, do this a few more times to increase your familiarity. (Although the caster can't be Off Target with the spell greater teleport he still rolls on the chart for the 5th-level Sor/Wiz spell teleport [conj] (PH 292-3) when using the spell greater teleport because the possibility for a Similar Area or Mishap remain). Use this accumulated information as the destination for the spell greater teleport. Alternately, get all the information needed to use the spell greater teleport by targeting the acquaintance the 8th-level Sor/Wiz spell discern location [div] (PH 222).

If you can neither find a reliable description nor contact a friend, you're left with either getting a detailed description the hard way or getting a particularly precise map.

Getting a Detailed Description

First, find a creature who's been where you want to go. Then extract the detailed description from the creature's mind.

"What?!"

The DM's made it clear that no amount of book learnin' or other research will do. The only remaining (even semi-)reliable descriptions are the memories of creatures who have been to the destination to which you want to teleport. Have the caster who is going to cast greater teleport use one or more of the following spells on that creature.

• The 2nd-level Sor/Wiz spell vision of fear [div] (Dragon #333 73), for 24 hours, grants the caster firsthand knowledge (suitable for scrying attempts and teleport destinations) of the caster's choice of either the target's most recent fear or the target's greatest fear. Note: That's awfully specific, though, but waiting by the docks or the trading post and interviewing recent arrivals from the region might find a suitable target.
• The 3rd-level corrupt spell absorb mind [div] (Book of Vile Darkness 84), for 1 min./level, grants the caster, after eating a portion of the dead creature's brain, "the creature's memories and knowledge to some degree, so that she has a 25% chance of recalling any important fact known to the creature." Note: I house rule this to 1 attempt per minute. The spell often requires me to ad lib the ridiculous.
• The 6th-level Sor/Wiz spell probe throughts [div] (Spell Compendium 162), for as long as the caster concentrates up to 1 round/level, grants the caster the the ability to "learn the answer to one question per round, to the best of the subject's knowledge.... and the answers to those questions are imparted directly to [the caster's] mind."
• The 7th-level Clr spell brain spider [div] (SpC 38), for 1 min./level, grants the caster, among other choices, the ability to eavesdrop on another creature's thoughts and learn that creature's "thoughts and memories... in detail."
• The 9th-level Sor spell mindrape [ench] (BV 99) grants the caster the ability to "enter... the mind of a creature, learning everything that creature knows."

One of those should get a description that's sufficient for the spell's caster to also use the spell greater teleport, but it's possible the DM may rule it's also necessary to retain this information perfectly to teleport accurately. If that's the case, use the following spell.

• The 3rd-level Sor/Wiz spell magic memory [div] (Wyrms of the North column "Deszeldaryndun")¹ grants the caster the ability to "absorb the sights, smells, sounds, tastes, and/or textures of [the caster's] immediate environment and magically record them in... memory." Then the caster "can later share [the] experience with another willing living creature simply by maintaining direct physical contact and letting the memory replay." Note: Confirm first that the DM allows this method of memory retention to work with another creature's memory. (I allow it to do so in my campaigns.)

Obviously, the spell magic memory is also useful if the caster who acquired the information must relay that information to the caster of the spell greater teleport.²

Getting a Particularly Precise Map

The skill Gather Information has this covered. It says

If you want to find out about a specific rumor ("Which way to the ruined temple of Erythnul?") or a specific item ("What can you tell me about that pretty sword the captain of the guard walks around with?"), or obtain a map, or do something else along those lines, the DC for the check is 15 to 25, or even higher. (PH 74).

Emphasis mine.

I'm guessing it'll be that even higher. In fact, I'm guessing the DM will just say No. If that's the case, while there are other magical maps in D&D 3.X,³ what's needed is this one:

• The held item Keoghtom's spidery map (Dragon #359 72) (26,400 gp; 0 lbs.) grants the bearer the ability "concentrate upon the map, searching [his] mind for a location, creature, or object. The map then acts as a find the path spell, showing in great detail the shortest, most direct physical route to the specified destination. [The owner] can only use the map once per day, and all other paths or locations on the map appear as an ever-changing blurred mass of webs."

The spidery map uses an effect like the 6th-level Clr spell find the path [div] (PH 230)--which has no distance limitation--, and it provides a destination--the crucial yet poorly defined thing necessary for employing the spell teleport et al. ("The spell instantly transports you to a designated destination..."). Pick the creature you know or the artifact you're aware of and activate the map (borrow a map from a friendly contact if its cost exceeds your funds--you only need the map once).⁴ That should be sufficient to use the spell greater teleport to get you where you want to go.

Alternative Means of Investigation and Travel

The 6th-level Sor/Wiz spell scry location [div] (Complete Scoundrel 102) is nearly impossible lest one possesses some connection to the location to be scried. The 6th-level Sor/Wiz spell shadow walk [illus] (PH 277) only allows travel at 50 MPH (that's, like, a week-long road trip on the Plane of Shadow--have fun!), but a level 12 caster can employ the spell phantom steed [conj] (PH 260) to go faster than that, and the 7th-level nomad power dream travel [psychoportation] (Expanded Psionics Handbook 96-7) goes faster than that--but navigation's an issue with a poorly drawn continental map (e.g. "We're going to California!" doesn't actually narrow it down that much). The DM will probably demand a familiar destination for the spell plane shift [conj] (PH 262) et al. because if folks could use the spell plane shift twice rather than risk greater teleport once, I expect most folks would; ask the DM.⁵

"Why Is This So Difficult?"

The ability to teleport to places with which one's already familiar is incredibly powerful. That the spell greater teleport eliminates both the distance limit ("I can see the moon, right?") and the possibility of being Off Target really is sufficient to call the spell greater teleport. Adding the ability to teleport to places unseen--if reliable descriptions or particularly precise maps are easily acquired--hurts the verisimilitude of many campaigns.

It's also possible the DM wants the PCs to reach the destination the old fashioned way--booking passage on a ship and sailing away or hiring a guide and riding hard--rather than allowing the blind teleport. It could be it's the journey that counts, not the confrontation at the end.

You should probably ask the DM if he wants you teleporting there. Maybe the plot is the PCs getting to the destination.

1. The column appears not to be archived. Here's the spell.

   Magic Memory

   Divination [Mind-Affecting]
   Level: Sor/Wiz 3
   Components: S, M
   Casting Time: 1 action
   Range: Personal
   Target: You and one other living creature
   Duration: Special
   Saving Throw: Will negates
   Spell Resistance: No

   You absorb the sights, smells, sounds, tastes, and/or textures of your immediate environment and magically record them in your memory for as long as you concentrate (up to 1 round/level). Anything that causes you to break your concentration ends the record. You can later share your experience with another willing living creature simply by maintaining direct physical contact and letting the memory replay. For as long as contact is maintained, that creature's senses perceive the earlier recorded environment. Once the memory is replayed, the spell ends, and the memory becomes a normal memory for both you and the target.

   Arcane Focus: A mind flayer tentacle. Note: Fortunately, no gp cost. I didn't want hard-up-for-cash mind flayers selling their tentacles to the wizards' college.

2. The only other ways to get perfect memory in D&D 3.X that I'm immediately aware of are the prestige classes Jordain vizier (Shining South 33) and shadow scout (Oriental Adventures 44)--neither of whom are casters--and maybe the cerebrex (Dragon Compendium Volume 1 72)--whose eidetic memory is a numerical bonus instead of actual memory--, although there very well could be other prestige classes or an infusion, mystery, power, soulmeld, utterance, vestige, or something else that does so. The skill Autohypnosis (XPH 36-7) only allows memorization of "text..., numbers, diagrams, or sigils;" ask the DM if a map's a diagram.

3. There's the map of unseen lands (MIC 164) (5,200 gp; 0 lbs.) and the greater and lesser underdark maps (DrU 77 and 76) (major and minor artifact; 0 and 1 lbs.)), for example.
4. The spell magic memory works for memorizing the map, too. Unfortunately, the 0th-level Sor/Wiz spell amanuensis [trans] (SpC 9) "copies only nonmagical text, not illustrations or magical writings."
5. Or not. You're in the DM's hands because of 5d% miles off one always is when using the spell plane shift (unless you've greater plane shift [conj] (SpC 159) and a previously visited location). There're not-nice folks on every plane; don't expect to arrive among pleasant folk unless the DM wants you to.

There isn't anything in the RAW that specifically handles this, but there are (as I can see) two ways a DM can rule this.

Option 1, the simplest:
Simply change the wording of staggered to read

... one simple or advanced action.

This would leave the effect of the status relatively unchanged, possibly allowing a few more actions to be performed than before.

Option 2, the specific:
With this option you change the wording to read

... a single attack, or move action, or cast a standard action* spell.

With the sub-note that the spell action economy can he faster, such as a quickened spell etc.
In this scenario you are pretty close to allowing everything the old/original staggered condition allowed for, but with the error margin being on the other side. In that there are some actions that were permitted in the "old" rules, that doesn't fit the new description.

Which of these two options should be used it totally up to your group, if you are indeed using the new action economy. My personal preference, however, might be with the first. Not only for its simplicity, but also because it's always better to have more options (as a player). :)

PS: There are, of course, variations and degrees of these two options. Taking rule #0 into consideration. ;)

PPS: Link to the unchained action economy