Third Avenue from the 20's to the 30's is "bar central." I don't drink, but...
Molly's, b/t 22nd & 23rd, is where we go for excellent burgers.
The Hairy Monk is on the corner of 25th.
The Mad Hatter is b/t 26th & 27th. In its previous life as a bar/restaurant called Caliban, we used to go to dinner there when they had -- believe it or not! -- a French chef. The menu now is your common bar food, i.e., burgers and such. They have a nice back garden.
Vertigo is on the corner of 26th. Looks to be a sports bar.
Choice Kitchen & Cocktails, b/t 27th & 28th Sts. We stopped in for lunch once. Had salads, which were huge and quite tasty. Very attractive atmospherics.
A new bar, Arctica, opened a couple of weeks ago practically next door to Choice. When I passed by the other day, I noticed they've plastered their menus on the front window and are touting their lunch special.
Tonic is on the corner of 27th St. (or maybe 28th?).
Joshua Tree is b/t 34th & 35th. A mini-chain. http://www.joshuatreebarnyc.com
I should also add one other that is not on 3rd. Waterfront Ale House is on 2nd & 30th. Very good food, especially the burgers.