Travelling the East Coast

Hi,

I was wondering if anybody new a cheap way of travelling from New York to Miami either by Bus or train? I will be flying from Sydney to NY mid april and heading up to Boston for the Marathon, then i wanted to make my way down to miami as im flying out at the start of May. I was thinking i would like an unlimited bus ticket that allowed me to jump on and off as i please so i can see places like Washington, Savannah and maybe even New Orleans and Memphis if i get time.

Has anyone heard of something similar? Or even if you have any tips at all about the east coast i would love to hear them.