Ooooh...I'm in NYC. 4th of July weekend should get GREAT bills. You are in for a treat! That being said, the true punk scene in New York is in serious trouble. Not that there isn't great music, and places you will totally be fine in. You just have to work harder than you did 10 years ago to find it.
Check out Southpaw in Park Slope Brooklyn first. They get A+ national and local acts there, but the neighborhood isn't really a punk/rock scene. That being said, Southpaw will still bring them in.
If you are staying in Manhattan, Williamsburg is one stop into Brooklyn on the L train making it convenient. Its the heart of the club scene in the city (that won't cost you $30 on Ticket*******) but the big scene in Billy Burgh is the emo hipster scene (which kinda grates on me) but try the Charleston on Bedford and North 7th which is a real good punk venue depending on the day. Death by Audio on South 2nd @ Kent has a good punk scene (its a bit of a walk from the train though.) Also the Glasslands next door to Death by Audio is ok because the book great local acts (more garage than punk) but everyone here always looks super upscale dressed down. Union Pool is the biggest spot in Billy Burgh and its always crowded as **** (its not always punk though, so double check since its a bit out of the way.) But the crowd isn't as punk as the punk bills would suggest. But its still a good spot.
Otherwise, in Manhattan, check out ABC No Rio (they have a website I think.) The last of NYC punks live there. Mercury Lounge on the Lower East Side Manhattan is always a safe bet for more rock. So is Otto's Shrunken Head and Luna Lounge and most often the Knitting Factory. But with the demise of the punk scene anchored historically by CBGBs, you get a lot more avant-garde or indie rock stuff in Manhattan than anything else.
If you don't mind spending money, The Fillmore-Irving Place and the Highline, and Hammerstein Ballroom will have good shows on 4th of July weekend.
When you get into town, grab a Village Voice (free in the red boxes all over the city.) And bookmark this site. http://www.myspace.com/nycpunk
This will help a lot.
Good luck! Enjoy our fine city!