Cheap or Free:

Parks and Gardens:
Central Park (Manhattan) The infamous park of New York City. If you go to one of the museums near the park, why not check it out? Strawberry Fields is on the west side of the park, near the West 74th Street entrance, if yr so inclined. [ www.centralparknyc.org ]
The Brooklyn Botanical Gardens (Prospect Heights) is free on Saturdays from 10am - Noon. Get in the gates before Noon, and stay as long as you want! - [ www.bbg.org ]
Prospect Park - This park is just as beautiful as Central Park. If yr in the neighborhood, it is more than worth a stroll. [ www.prospectpark.org ]

Various Others:
Walk across the Brooklyn Bridge! If it's a nice day (and we are hoping it is...), take a walk across the pedestrian level of the bridge and get a great perspective on the city and the Hudson Bay! It takes about 45 minutes if you are casually strolling. Bring yr cameras, and watch out for the bikers!

Take a boat tour of New York City. Circle Line Cruises offers a variety of boat tours of the New York harbor. There are lots of options, but I would suggest either the two hour Semi-Circle cruise, or the two hour Harbor Lights cruise (the only difference is that the Harbor Lights tour is at sunset, so you see the city at night from the water). Each tour is $27. [ www.circleline42.com ]

Rent a Bike. You can either rent it with a tour guide, or do it on your own. [ www.centralparkbiketour.com ]

Free Kyaking. Kyaking in the city? You Bet! [ www.downtownboathouse.org/programs.html ]