Other people here know more about the Princeton area, so if there is something else available, I'll leave it for them to mention. I know there is parking at Princeton but its not a huge lot and I have no idea of the rules.

The place I know about to park is MetroPark. That is at the intersection of the turnpike and the garden state parkway, I forget the exit #s. They have a big garage there and shouldn't be a problem leaving your car.

The ride into the city isn't too far from there so NJTransit is fine. From PA, my personal preference would be Amtrak for the more comfortable ride.

Enjoy your trip.