Thanks to all who responded to my post.
We are actually flying into St Petersburg airport since we're flying Allegiant Airlines. We plan to take a cab from St Petersburg Airport to the Embassy Suites downtown Tampa. (We're flying in the day before the cruise) I'm sure the cab won't be cheap...but rental cars are worse than a cab if you're not returning the car to where you picked it up.
When the ship gets back in on Saturday morning, we're renting a car and driving back to St Petersburg for the day and flying out the next day. We're renting through AVIS.
So our first night in Tampa we'll be without a car, but staying downtown at Embassy Suites and it looks like there's plenty to do within walking distance.
Any suggestions while we're in St Petersburg/Clearwater area?