I’ve taken Chinatown buses between NYC and Baltimore, and they were always fine. Cheap, usually on time, and the passengers were generally a mix of Chinese people, overseas backpacker types trying to save money, students, and working-class people who didn’t want to pay Amtrak prices. I don’t remember any shady characters or unpleasant experiences, except the time when a combination of a closed tunnel and rush-hour traffic meant getting stuck in Manhattan traffic for two hours at the start of a trip. I assume there are Chinatown buses that run between NYC and Philly.
Of course, if you don’t mind spending a few extra dollars, Amtrak really is a nice way to travel. The seats are comfy, plenty of legroom, and it’s a pretty fast trip. Not sure exactly how much the NYC-Philly trip costs, because the reservation and ticketing section of Amtrak’s website is currently down.
Another option, which might be a good compromise between the convenience of Amtrak and the cheap price of the bus, is regional transit. You can get from New York to Philadelphia using the New Jersey Transit system from NY-Penn Station to Trenton, and then get on a SEPTA train from Trenton to Philly. Check out the SEPTA and NJ Transit websites. I believe that, when you get on the NJ train in New York, you’ll be able to buy a ticket that takes you all the way to Philadelphia.
You can plan your NJTransit/SEPTA journey here. You want to leave from NY-Pen Station, and arrive at 30th Street Station in Philadelphia. I just checked it out, and it takes about two and a half hours, and costs $12.50 one-way.
In Philadelphia itself, much of the main tourist stuff is perfectly easy to do without a car. Basically, most of it is in the Market/Chestnut/Walnut Street corridor that runs east-west between the Delaware River and the Schuylkill River. Map here.
In this area, you’ll find much of Philly’s historic stuff, including the Liberty Bell, Independence Hall, City Hall, the Second Bank of the United States, etc., etc., as well as some lovely old houses and pretty streets. Wander a few blocks further south to South Street, and you’ll find some interesting shopping, bars, restaurants, and the ubiquitous Philly Cheesesteak. If you go north-west along Benjamin Franklin Drive from City Hall, a 30-minute stroll (or a short bus or taxi ride) will take you to the Philadelphia Museum of Art, which is one of my two or three favorite art museums in the United states. The collections are fantastic, and as a bonus you can run up the front steps and raise your arms in an imitation of Rocky Balboa from the movie.
All of this stuff is easy to do without a car, and there’s a pretty decent subway line that runs east-west right along Market Street and will get you back to 30th Street Station when your visit is over. This area is also, in my experience, generally pretty safe. Of course, Philly is a big city, so you should be a bit cautious when walking around after dark, but i’ve never had any problems in any of these tourist and historic areas.