They are close together, but sightseeing in the city of Trenton is unlikely to be very satisfying. It is not the loveliest place. There is some Revolutionary War historical stuff in the area (most of which is better done with a car): see the Trenton Historical Society website for information.
Princeton is a much more congenial place, but I'd venture that the sightseeing opportunities there are also pretty limited if you do not have a car. You can wander around the university, some parks, and the historic district, but beyond that...I don't know. See Visit Princeton.
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