We live in Richmond, S1 attends P'ton and all of our family is in NY. If there are a bunch of people involved, I would definitely rent a minivan and drive. As long as you leave the DC area by 3 or after 6:30-7 p.m., it's really not that bad and would probably wind up being alot cheaper and much less hassle than Amtrak. We used to take the Baltimore Washington Pkwy years ago, but now find it much quicker to just take 95 straight up (due to 65 vs 55mph speed limits on the two roads) to 295 which you get on just after the Delaware Memorial Bridge (keep to the posted speed limit on the bridge, they like to ticket as you come down the hill). Don't take the Jersey turnpike, there's no need to pay tolls when you can do that part for free. I95 can also get you to Rte 1 near Princeton, but it goes around Philly and can be a bit more crowded (but you get to see the Philly skyline).
Oh yes, be prepared to pay a few tolls, ie have cash or an EZ pass with you.
If you take the train, definitely take it to Trenton and then switch to NJ transit (
New Jersey Transit - Home) to Princeton Junction and then the dinky from there. During the day, the dinky runs about every 10 minutes, but at night only about every 30 minutes. Also, the only really close hotel to the dinky and campus is the Nassau Inn, but it's an uphill hike from the dinky station and would not be fun with luggage, so I'd get a cab.
As others have said, most of the hotels are north of the campus and you'd need a car or taxi. There is Hampton Inn, Marriott, Courtyard, Homewood Suites, etc and many give discounts if you're there to visit campus.
Another thought would be to stay in Arlington that night and leave at 5 a.m. the next morning. Traffic flies at that hour. I think if you drive you should plan on a minimum of four hours. The quickest we've ever made it was five hours from here, at five in the morning, with no stops and we're about 75 minutes from Arlington. Oh and gas is cheapest in Jersey and then next would be VA.
Feel free to pm me if you have more questions.