I would highly recommend the Embassy Suites Downtown. They don't have a shuttle from the airport, but the United Cab taxi was a flat fee of $25. I was just down in Tampa the beginning of June for a long weekend. This hotel was great. You get breakfast and a managers nightly reception. It is so convenient to everything. Right outside the door is a trolley stop. You can ride the trolley all the way down to Ybor city for more shopping and restaurants/pubs. The trolley goes right by Channelside (Tampa Aquarium, more shopping) and the port. I asked the trolley driver if you can bring suitcases onboard and he said yes. So the morning of the cruise you could take the trolley to the port or just grab a quick taxi. The trolley cost $2.50 one way or $5.00 for an all day ticket.
We went to Busch Gardens and used "Blue One" shuttle. click here
They picked us up at the Embassy Suites and took us to Busch Gardens. It was $30 for two people one way. You can call them about 30 minutes before you want to leave Busch Gardens to come pick you back up. Check Busch Gardens website for tickets. I got our tickets with the meal plan for the same cost of a one day ticket. The meal plan worked out well.
There's also a Marriott downtown right across from the Embassy Suites. Both of these hotels are right next to the Conference Center and the Tampa Time Forum where they have concerts and events.