That's not easy and will eat up valuable time waiting for buses. Look at redcoachusa.com to see if they provide service to the areas you want to go. You'll have to add cab fare to the cost of the bus service.
Between Miami and Key West you can use the Keys Shuttle (keysshuttle.com)
There is a Greyhound, but renting a car is the best/easiest way if you can swing it.
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