Central Park deserves a separate guide. Not only for its size but for the number of things to do in and around it!
If you took out the NEW YORK PASS, pay attention: It includes a free bike for 1:30hs at a place one block from the park. Check this before renting and pay it elsewhere.
The best advice is: Go through it as much as you can. Either by bike or on foot. If you have time, try dedicate it from early to no, not just for a little while,
Be sure to visit The Loeb Boathouse restaurant and if you can have lunch there (it's not cheap, but if you have a budget it's beautiful and you eat great with a nice view of the lake). You can also take a boat ride and live a different experience!
Another option is to take something to eat and go to the park for a picnic.
If you go in summer, we recommend going to the park in the morning because of the heat! It is huge and with the bike it can be exhausting.
Inside Central Park you can find the famous Strawberry Fields. It's nice to stay for a while listening to an artist who is always out there paying tribute to the Beatles with some music. It's on the Upper West Side.
One way to take advantage of this day is to go out the park at some points to see some other main attractions that you have nearby and then entering back in.
For example, you can find the Columbia University outside the park in the Upper West, you can visit the campus and low library.
Also, on the East side, if you continue on 5th Av. along Central Park, you will arrive at the Metropolitan Museum (MET): 1000 Fifth Avenue at 82nd Street. It is closed on Mondays, except Holiday Mondays.
If you're not a big fan of art, maybe you can go just to see the building, which is impressive, because the museum is huge, it takes you almost all day to go through it! It focuses on Greek, Roman, Egyptian, African, Oceanian, Middle Eastern, Byzantine, Islamic art and you also have sculptures, armor, a library... it's infinite! Ideal for a rainy day.
A few blocks away you have the Guggenheim museum, with its psychedelic construction. On Thursdays it usually closes but we recommend checking out the schedule before you go. You can also choose to stop by to see the building from the outside if you are interested in architecture or design.
Going back into the park, just walk around all the little streets, tunnels, sports parks, lakes, zoo, sit for a while there... BREATHE IT!