Having no idea how long you'll be here or anything, I'd say the best thing to do would be to hop between DC, PHL and BOS using Acela or Amtrak Regional depending on your budget.

Then in each city you can use rail or rent a car to hop between the close schools.

Penn is walking distance from the station in PHL so that's one you can definitely hit. GW is a short walk from a Metro station in DC so that's easy too.

If you want to be adventurous you can drive to Ithaca to visit Cornell. It's about 4 hours from either Philadelphia or NYC. If you want to visit a school in NYC then you can hop on the Campus To Campus bus from NYC to Ithaca. I wouldn't take any other bus to Ithaca. I did Greyhound once and really don't want to ever again. Otherwise for about the same price you could rent a car in PHL after visiting Penn and drive up to Ithaca. It's a really easy drive.

May is an odd time to be visiting schools. Most graduation ceremonies take place during May so hotels and travel to these schools might be much more expensive than normal. Keep that in mind. Having gone to Cornell I know that prices skyrocket around big events on campus. They're already overcharging for most hotels around the area in my opinion, so during events it can get ridiculous.