How can you travel from Daytona Beach to West Palm Beach without a car?

You can if you can get from Daytona Beach to DeLand. There are two trains a day each way between DeLand and West Palm Beach.

You can take connecting Amtrak Thruway service from Daytona Beach to DeLand provided by the Southern Komfort Cab Co. It can be picked up at the Hilton Daytona Beach/ Ocean Walk Village.