Greyhound is a Bit Flexible
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While it will cost more than a single straight through ticket, it is possible to take Greyhound between almost any two cities you could name along the east coast. You would, for instance, buy a ticket from Atlanta to Jacksonville, then one from Jacksonville to Daytona when you were ready, and so on down the coast. As a round figure guess on what this might cost, I'd say about $200 based on today's fares and a handful of stops. The total cost will go up a bit with each additional stop. Remember, that's one way and it won't nearly be as fast as you think. The run from Atlanta to Jacksonville takes around 8 hours rather than 4 because the bus will be stopping in many small towns and cities along the way. If there are two of you and you'll be returning to Atlanta, then the $600 for the car (plus fuel) starts to get competitive with the nearly $800 for two sets of tickets that add up to two roundtrips between Atlanta and Miami. Unfortunately, those really are your only two options for doing what you want.
AZBuck