I haven't been yet (meant to go on my last trip, but never got to it):
http://www.barcadebrooklyn.com/
been there they have a ton of arcade machines old school...expect it to get super crowded around 10 pm and on.
a couple of good places to grab some food:
Pauls
On 2nd ave between 7th st and St. Marks(8th st)
Amazing Burger joint!!
Tio Pepe's
4th St just west of 6th Ave
Great Mexican food
Avoid the upper east side or the west village for bar hopping unless you are a frat type of guy
The east village(3rd ave to avenue B between 14th st and houston) has lots of great bars with less people looking to pick up your wife!
LIT a bar on 2nd ave between 5th and 6th streets (there isn't a sign out front) has some great Karaoke sunday nights 11pm until 4am
Crocodile Lounge on 14th st between 1st and 2nd ave has free pizza all the time with each drink, they also have skeeball in the back area, and a buck hunter machine.
Cheap Shots on 1st ave between 8th and 9ths has an air hockey table, and $5 car bombs on friday nights
These are all what alot of people would consider "dive" bars, which means your not gonna get alot of the popular music playing nowadays...more rock and roll style type of places.
Great free (2 drink minimum) jazz music, increasing hard to find the free jazz in nyc,
http://www.arthurstavernnyc.com/ very mellow, and great musicians!
I can probably think of more if you need more options...or anything specific.