Can Princeton and Trenton be done in a day?
 

Also are both cities accessible from Philadelphia? Or I should go from NYC? What's the cheapest way to get there from Philly?

Both places are accessible by train from Philadelphia.

What are you looking to do in Trenton and Princeton? Business? tourist exploring?

Just doing sightseeing. I looked at the NJ Transit map yesterday and they appear to be very close together. I thought I can possibly explore both places in a day if I leave early enough.

Princeton is a lovely town with great stores and restaurants. Trenton on the other hand is not..

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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From NYC, Megabus offers service to Princeton. Fares can be less than what NJ Transit charges for rail travel.

Also note that rail travel to downtown Princeton requires a transfer to a shuttle train ("The Dinky") at Princeton Junction rail station.

Agree that Trenton is not much of a spot for tourists arriving by train. It's a pretty beat up city.

I'd stick with Princeton for a day if you are there. Lots to see, good shops and eateries, interesting tour of the campus, etc.