Amtrak trains are a comfortable and cheap way to travel. Schedules and routes are not the best if you want to visit a lot of places, but if you want to travel to specific destinations, it’s a really good choice.
They have something like the European Interrail call “The Rail Pass”. The USA is divided in several areas and you can buy the most convenient pass for you: you can choose the areas and number of days you want.
Go to Penn Station to buy one (or buy it on their website).
Rail Pass
fifimagoo added
This is not a good option if you are spending most of your time in New York City. The USA is a huge country and most of these trains are expensive and take hours to get to the desired location. Also, the rail pass does not include the "high speed" train between NYC and Washington DC (Philadelphia, and Boston too) - Acela Express.
http://www.amtrak.com/servlet/ContentServer?c=Page&pagename=am%2FLayout&cid=1241305460725
