How might elven societies be different from the norm?
I wasted a silly amount of brainpower thinking about that kind of question back in the day. This was back when elves lived like a thousand years, were all Chaotic Good, 'high' elves were the typically-woodsy sort, 'wood' elves xenophobes, more civilized/ancient 'grey' elves fading into legend, &c, so take it with a grain of salt...
In what ways would an elven city be different than a human one?
They just wouldn't have 'em, is what I concluded. They like living in harmony with nature, they're very long-lived, and they haven't overpopulated the world, so they likely have very low fertility (or very high mortality from fighting orcs &c, or practice infanticide, take you pick, I went with conscious-choice low fertility: elves conceive only if they really want to, and often not even then, or after decades of working at it).
'In harmony with nature' for a humanoid species means a foraging lifestyle, elves are well-established as living in the woods, which isn't bad for that kind of thing, and I pictured elves as not needing a lot of food in the first place, but their populations wouldn't approach those of a city, certainly not in density.
For example, since elves don't sleep, would they even have bedrooms?
I doubt they even have building in the conventional sense. In my campaign world back in the day, elves talked to and magicked trees into growing into shapes that provided shelter for them, literal 'treehouses.' The trancing instead of sleeping thing was a little later, based on the sleep/charm resistance, and, IIRC, came from an old Dragon article that also suggested elves should have ultravisions (low-light) rather than infravision (dark-vision). So no bedrooms, per se, meditating or trancing might be done under the stars, or during the day, in a deep thicket, if you go all the way and figure elves are naturally nocturnal (as you might expect from an above-ground critter that sees in the dark).
I imagined them having a general expectation of hospitality among elves, and extending that to other species when it seems right (which, since they tended towards CG back in the day would be often). But an inn in the traditional sense? Only at the edge of a community, as part of some sort of trading outpost.
Would elven cities be surrounded by small elven "farms" that support it with food?
Maybe horticulture. Elven woods might have an abundance of edible plants because elves coax and persuade and enchant them to grow there, and a relative lack of pests afflicting those plants because the elves use glamour to get them to go elsewhere (like human agricultural land). But cleared agricultural land? Fields? Enslaving livestock for food? No. Icky.
I'm a bit torn, because on the one hand I want the city to make sense given what elves are like, but on the other hand I don't want to have to create an entire city from scratch and force my players to learn how it all works.
If it's not fun, hand-wave it. Print out a picture of Rivendell off the internet, and leave it at that.