3 Ave, Gramercy Park

I don't recommend living on avenues if you can, at all, help it. And, 3rd is no exception. There are too many people, too much traffic, no neighborhood feel, etc. But, living off of 3rd in Gramercy is not too shabby. There's a lot going on in the 3rd Ave realm which you don't often find on the East side above the East Village.
There are a few cool bars on 3rd at 23rd that start to lose the Kip's Bay (no man's land) feel. Bull's Head Tavern and Molly's are both great. There's also a vintage store, a yogurt shop and a couple of little restaurants on the block so you definitely don't have to travel far to eat, drink and be merry. The next block down has some ugly as sin looking apartment buildings, but there are also some lovely little gems such as Black Bear Lodge, Copper Door Tavern and a really cute wine shop.
The oldest building in the neighborhood is right at the corner of 21st and 3rd (it's from 1832) and there's a spa on the ground floor. Nothing like ghosts with your massage, huh? This block has a ton of neighborhood conveniences like a pharmacy, dry cleaner, market, pizza spot, and, of course, a few bars. I don't know who doesn't want to get a beer with their dry cleaning so this block is pretty useful. And, down at 20th there are, more bars!! Oh, and a lovely French restaurant called Piccolo Cafe.
Down around 18th there are more little conveniences on the ground floors of some of the ugliest buildings in the neighborhood. They all look like hospitals aside from Scheffel Hall. Scheffel Hall is a really beautiful building that had been a bar since the late 19th century where writers like O. Henry used to hang out. It's a pilates studio which I think is an absolute crime. How many pilates studios does one city need?
The block below 17th is really pretty and looks very much like the Gramercy Park that we all know and love. There are a lot of old buildings, trees and a sort of quaintness to the street which is really rare for any part of an avenue. All of the ground floor businesses are cute, little restaurants and I recommend Amai for afternoon tea. I wouldn't mind living in one of these buildings because they're just so pretty and old.
3rd is great because of all of the places to grab food, drinks, laundry . . pretty much anything. And, the area around 15th-17th is really cute so I would live around there if you have to live on 3rd. It's a pretty great Avenue and I don't often say that.