Diablo – What’s the best difficulty to farm a “Ring of Royal Grandeur”

Act 3 loot is the best in the game, so if you can farm these mobs consistently you totally should. The best areas I've found are:

• Underbridge (Rakkis Crossing waypoint then up and to the right) – This area spawns about 60-65% of the time. Guaranteed one elite and a possible resplendent chest. Find the elite, explore the small dungeon, and teleport out..
• The Keep Depths level 2 – The most elite dense of the three Keep Depths levels. Usually 4-6 elites found. Can be accessed by going to the Keep Depths level 1 waypoint and immediately going down a level. You will run into Soul Rippers here but they are a lot less potent post-1.03.
• The Keep Depths level 3 – Usually 2-4 elites. Smaller than the Keep Depths level 2. You can usually find an elite pack within 1-2 minutes near the waypoints.
• The Fortified Bunker – The Fortified Bunker or the Barracks will spawn outside the Arreat gate. It’s a bit smaller (and easier) than the Barracks but will have between 4-10 elites and a resplendent chest in level 2.
• Arreat Crater level 1,2 – 3-5 elites each.
• The Core of Arreat - 2-3 elites. Hulking Phasebeasts do spawn and can be very difficult. Skip them and face Azmodan if the Phasebeasts get particularly tough affixes.
• Tower of the Damned, Heart of the Damned - 1-3 elites per level (4 levels). Usually 2-3, although you can run into both Phasebeasts and Soul Rippers on some levels.
• Siegebreaker – An easy set boss if you can handle the reflect. Make sure you kill him after you have your five stacks. One reason not to do Siegebreaker is selecting his quest doesn’t give you access to all the that killing Azmodan or Cydaea will.
• Cydaea + Azmodan – Kill both if you can. Azmodan is extremely but post 1.03 Cydaea gives the Wizard/Demon Hunter serious. If she’s too much, just select the very last waypoint in the Heart of Sin quest and kill Azmodan once you have your five stacks.

Source: http://www.diablo3strategyguide.com/inferno-act-3-runs

Definitely add the Ancient Path waypoint to that list, as there's often a goblin nearby.

I'd also recommend adding Vault of the Assassin to that list. Although it can take a while to find, you'll bump into a few elites while trying to find it, and once you do, the vault guarantees you a good number of elites once you get there.

I agree that Kulle's lair just doesn't seem to have enough elites to make it worthwhile.

I spent some time doing an "ActII lite" run, where I'd get checkpointed in the VoA, clear it, then hit the Black Canyon Mines, Ancient Path and Road to Alacarnus waypoints and end it there, without bothering with Kulle at all. The time saved by starting inside the Voa each time make the run feel a lot more efficient. It might have been entirely subjective, of course :)