There are a couple of good gyms in the wall street area, one just off Broadway across from city hall, the other at 80 John street, closer to the seaport. Neither has a pool.
Go to bigger gyms uptown if a pool's necessary-23rd and 14th street:
Chelsea Piers, 23rd at the west side highway.
A chain of city-run gyms in manhattan, brooklyn and other borroughs that are a bargain. Join and have access to all of them. Here are some that have pools:
-23rd street east at FDR.
-25th street west between 9th & 10th ave.-very nice, brand new and not as crowded as 23rd.
List of NY-area gyms:
http://www.nycgovparks.org/sub_things_to_do/recreation_centers/rc_rc_by_borrough.htmlThe 14th street YMCA has a pool but is a lot more money than the city gyms and doesn't have the room or variety of Chelsea Piers.