I know some people do the PHL-NYC commute on the Chinatown bus. And for 19 days, with weekends, and I was in my early 20s I might survive it - but I hope you've got a couple of weeks downtime afterwards. I'd use the 6 from Chinatown unless the weather was really bad. There's also a bus that runs up Bowery/3rd Avenue that might work.

I've got to ask though, that if you've got big issues with living in NYC, is this internship a good career choice?