Is it a totally planned trip? Like, is everyone always in a group doing the same stuff everywhere or do they let you go in a certain area and tell you when you need to be back at "base"...or what have you?

I was there St. Patrick's Day 2003 for a band trip and it was amazing.

We were set loose in and around the following cool places:
5th Avenue
Radio City Music Hall
Empire State Building
Central Park
Time Square
WTC hole (that's mean)
Ellis Island
Staue of Liberty

Apart from going to Hawaii for band in 2005, this was easily the vacation with the most "holy shit I didn't think I'd ever get to go to these places" moments.