I make the trip pretty frequently...here are you options and prices...
1.) Amtrak from Penn Station NYC to 30th Street Station PHL. Takes about 1 hr 15 min. Cost about $80-$120 depending on when you leave (Sundays are expensive). When you check-out and it asks for "promotional code," enter - v688 for an extra 20%ish (note: this sometimes depends on which train you take ie. acela, regional, keystone, etc. just play with it and you can get the discount; might have to buy one way tickets each way)
2.) NJTransit to SEPTA Rail. The way this works is you go to Penn Station NYC and get on an NJTransit Train which takes you to Trenton NJ Station (90 mintes/75 if express). When you reach Trenton via NJTransit, on a different platform the SEPTA train will be waiting for you to take passengers right away to 30th Street Station PHL (40 min). At Trenton NJ Station, there is usually an 8-10 minute difference between NJTransit - SEPTA trains. The only bitch thing about this method is that if one train is running late, the next doesn't wait for you so you have to sit an hour for the next one (happened to me before). One way complete is 2.5 hours. Price round trip is $35 ($20 for Penn Station NYC/Trenton via NJTransit and $14 Trenton/30th Street PHL via SEPTA) Schedule for round trip is here:
http://www.septa.com/service/sched/pdfs/R7.pdf
3.) Chinatown Bus. I just took this for the first time and though I don't like buses that much, this is my new way for making the trip. Bus takes you from Chinatown NYC (basically City Hall/Brooklyn Bridge Subway Stop on the 4,5,6) to Chinatown PHL (11th/Filbert or about Center City). The cost is $20 round trip if you buy it at once ($12 each way separate). The time is approx 2 hours. Bus usually not crowded if you leave mid day (10a - 2p).
4.) You could always fly for fun...
Regardless of the method, once your in the city, I would recommend taking the subways to the schools from your hotel or train station if your making a day of it. They may look like crap but they are safe and its day-time. Plus they are only $2 vs the price of cabs. Both subway lines run to each school, UPenn or Temple.