There is a train that runs from Newark to NYC, it's fairly cheap. Last time there I stayed in Queens, didn't mind taking the subway. Our hotel picked us up from the airport. A week long subway/bus pass was $24. Have fun in NYC, love going there.
Well if you do decide to goto Cleveland, let me know I can give you info. The Rock hall is cool, very expensive but worth a visit at least once.
Yes you need to goto Amoeba records in LA. If I let my self could have easily spent hundreds there.