I like the Cloisters idea. On the way, I recommend you walk up Broadway up to the 80s starting at Lincoln Center and marvel at the architecture of the apartmen buildings. Just fantastic. Then head over to Riverside Park and go for a nice walk. After the Cloisters, head to the northern most part of Central Park and walk around. Rock climbing, beautiful pond, walk around the area. Walk the entire circumference of the reservoir. Great views of the CPW skyline on the eastern part of the walk.

Do you play tennis? Call the National Tennis Center and reserve a court for an hour of play. How fun to play on the same surface as those in the Open. If you want to play at either Riverside Park (on clay) or in Central Park (mostly Har-Tru), purchase a single-play permit at either location and make a reservation for court time. These permits are for same-day play only. Arrive early.