Not sure if these fit your criteria, per se, but here are some bars I like:
(1)
HiFi. Resonably priced, has a great happy hour and is generally not too crowded on weeknights which is awesome if you want to play pool. There is at least one very cute bartender, oh, and also
the greatest jukebox known to man.
(2) 2A. Corner of 2nd Street and Avenue A. Also reasonably priced & with a good happy hour (with bonus free popcorn!), and fairly laid back until 10 or 11, at which point you can count on it getting kind of insane.
(3) The Magician on Rivington & Essex. Totally laid back and unpretentious, generally lacking in white belts and footless tights. Can't remember what the prices were like.
(4) The Crocodile on East 14th. Um, they have free pizza and a photo booth. I'm not sure what else you need.
(5) Ace Bar on E. 5th. Okay, this bar is kind of horrible and loud, but they totally have
skeeball. Pick your battles, that's what I say.