I suggest the hop on hop off bus tours in nyc.... when I went my friend and I were on a budget, so we grabbed a two day ticket for the tour buses. Not only was it a different experience every time (because each tour guide had different info to share) but it was waaaaay cheaper to get from one end of the city to the other than always taking a cab! AND you get to see pretty much all the major sights. Going to the top of the empire state building was my favorite (and this is coming from someone who is deathly afraid of elevators!!). Since my friend and I opted to do the Empire State Building we didn't go over to do the Statue of Liberty Tour, BUT We got great views from Battery Park and we also got some great views of her and the city by taking the Staten Island Ferry. Stopping at "Ground Zero" to take and have a moment there was also a must. Oh and Times Square at night for sure! Ok I think I'm done..... we spent a week in the city and I still never got to see it all, but we must have walked the length of Manhattan 20 times.... my feet were tired when we got home! LOL Oh, and I am a "scaredy" cat of everything and I actually felt very safe in the city.
I've never been to Philly, but I did take a side trip to PA on my NYC trip.... I took the bus, long but not terrible trip. Definitely take the train to be faster.