Getting to Princeton....
If you are flying - You can fly into Philadelphia Airport, Newark Airport, JFK or LGA and then take either NJ transit or Amtrak to Princeton Junction or get a car service/taxi.
If you are taking the train - You can take NJ Transit from Penn Station NYC, the Northeast Corridor Line to Princeton Junction. There are also Amtraks that go to Princeton Junction and Trenton which is nearby. You can take an Amtrak from NYC, Philly, Boston, Baltimore - basically anywhere up and down the East Coast. At Princeton Junction, there are taxis and ubers to bring you to your hotel.
If you are driving - there is ample parking throughout Princeton and in multiple garages in town (Hulfish & Chambers garages are closest). See picture below of the couple on a roadtrip....
Hotels: Our room block is at The Nassau Inn https://reservations.travelclick.com/13522?groupID=3229681
We would recommend -The Nassau Inn or The Peacock Inn in downtown Princeton. There is also a Hyatt Regency, Courtyard by Marriott and the Princeton Marriott a short drive away.