There are a few good hardcore gyms right in the city, and you can get a free pass for a day or three at most.
-Mid-City Gym is the classic old-skool gym. Draper used to train there once in a while before moving to Cali in the 60s.
-19th street gym at 22 W 19th between 5th and 6th. One of my faves, i recommend it.
-Steel Gym on 23rd between 6th and 7th, closer to 7th. Good gym.
-14th street gym between 5th and 6th.
-Gold's, around Times Square.
-Best gym to me is David Barton at 23rd and 7th if you can handle the gay clientele.
-Bev Francis is worth visiting, outside the city.
-Central Park on weekend afternoons until late, if the weather's good is a must-rent a bike or blades, run, etc. and good people watching for sure. Same thing weekdays but much quieter.
-Best places to sit down and people watch - Union Square, places like Coffee Shop, Blue Water Grill and Union Square Cafe, etc with good food and outdoor seating. Also upper west side on Broadway in the 60s across from Lincoln Center.