Well, for starters, I'd say don't use D&D. It is a game tailored towards violent conflicts, which is exactly what you're avoiding, it seems. Mind you, I said "violent conflicts". No story, thus no game, can exist without any conflict whatsoever. I'm not also saying it's completely undoable with D&D, just mainly... a waste of its design and practical goals. Another way to put it, to use a metaphor, is: smartphones are great, you can do a lot with them, they're like handheld computers... But they can't really substitute a desktop computer in every way, maybe not even most ways.
Now, if you're willing to work outside of D&D, there are some good systems out there for that "action and adventure doesn't mean swinging swords all the time" vibe you're after, like, for example, Fate (The Dresden Files RPG, Spirit of the Century, Diaspora, etc), in which most of the mechanics about resolving conflicts are the same, regardless if it's a brawl, a wardrobe and style show off or even an economic dispute between Lex Luthor and Bruce Wayne. It's worth a look, really, and there are SRDs available for some of those games (Spirit of the Century and Diaspora, iirc).
If you're sticking to D&D, plotting the campaign isn't the difficult part; the difficult part is to design encounters (which is just a way of saying "conflict scene") that allow your PCs to shine doing their thing when most of their sheets are geared towards combat (yeah, players do that, it being the game it is).
For the wizard (most hocus-pocus folks, really) and rogue, that's easy. Most other types, though, will rely purely on RP, most of the time, which isn't bad per se, just kinda unfair, since some players get to look at their sheets and say "I can do this, this and that", while the fighter's player has to memorize lines from Gladiator and the ranger's player has to become a living Bear Grylls encyclopedia.
If your group can pull it off, that campaign'd be the stuff of legends, but it'll be hard, really.
Background and Legacies
Outside the dungeons, pits, castles and sewers there is the chance to explore what the characters are more than just damage dealing machines, what they want to be their legacies, who they know, what they want to be; encourage players to expand on their backstories - or examine their backgrounds and see what can come out of the woodwork, not even as a battle but as someone to talk to or stories that they can find out about.
Relationships
High level characters should have not a small amount of fame and NPCs should be clamouring to apprentice/advise/woo/get money/kill them depending on what they've become famous for. Think Wizard duels to determine "the greatest magi of the land", building sage towers to tutor a school of magic, creating new religious movements, creating a guild of adventurers to solve all the petty tasks that no longer are worth the time, etc.
The world
At Epic level politics becomes an important factor; characters who are powerful can solve important problems, defeat enemies or swing wars between countries and Kings/Nobles/Wizards will want the PCs on their side - or rid of them - for wider political motives
Think scheming political figures "Have this castle as my thank you for your service" (said castle is crawling with dangerous bandits) religious orders that are asking for help with crusades and so on.
Making it alive
And those the players know will have moved on as well; NPCs shouldn't stand still, give a little snippet to important figures in the characters lives to make things feel more "alive", Bob and Bobette have had a baby, Duke Von Bob has created a new trade route, Trader Bob has partnered with his former enemy anti-Bob.
A world of shops and taverns?
Another thing to help the players feel a place is more alive is to add things to the city that are more than rumour-generation taverns and item-trading shops. Don't scattergun these in, you can drip feed them schools, colleges, magical research centres, masons guilds, graveyards and religious institutes to the point that (hopefully) they'll ask "is there an X" in town and then you can sit back and stuff in some generic NPCs for X, give it a name and have them talk to a piece of the city that they've effectively generated for you. Now that's lazy GM'ing and I like that :)
PC: "Is there an alchemist in the city?"
Me: (Checks list of random npc names, rolls a dice for personality on a quick chart), writes 'Alchemist, gruff, slightly mad, level 15' "Yes there is, a few inquiries tells you about Old Bob the Alchemists shop of chemical wonders, it's down old goat street."
Best Answer
You say that "I don't think it makes sense to just outright tell the players", and others may feel the same, but I do not agree. Unless the text in question was written in code, anyone reading through it will obtain the information. So the only question is: how much time does it take to find the relevant passages?
If the reader knows what to look for, it will be a simple matter that could be done during a short rest for example. If time is an issue (say, the guards have raised an alarm and they can't take the book) calling for an Int(Investigation) check would be appropriate.
If they do not know what to look for, maybe just have a hunch or hint that something interesting might be in it, it will take more time, lets say 8 hours to read the whole thing. That will take a day of downtime or 2 long rests for an elf. (Hey, we made use of the Trance feature!)
If the thing was written in code, assume the writer has the Linguist feat (PHB 167) and calculate the DC accordingly to crack it. I would recommend that doing so takes 8 hours of light work too.