The system of running/bike trails by the hotel is great for both shorter and longer runs. There is good trail running at the Institute Woods, or along the Carnegie lake that continues as the D&R Canal. These trails are also suitable for mountain bikes.

The D&R canal by Princeton University has kayaking and canoeing.

Princeton University has a free art museum, and offers campus tours. Albert Einstein's house is close to the university at 112 Mercer Street, but it's not open to the public. Grounds for sculpture is a short drive away. Princeton Battlefield State Park is great for picnics, strolling about, and kite-flying. visitprinceton.org has lots of information about these and other options.

... is right inside the hotel.