I will be flying JetBlue into Tampa and have a car rented through Budget. Where do I pick up the car ?

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at the airport take a train that takes you to the rent car center

You have to take the Skyconnect train from the main terminal to the rental car center. 2 stops and you'll be at the rental terminal with all the major rental companies there. You walk to the budget desk and once you are done with the data registration and payment, you'll fine the car in the parking lot. Car keys will be inside the vehicle.

Just follow the signs to the rental car section I believe you have to take a tram to get to the rental car section. Once you have all your paperwork frkm the Budget agent they give you very good instructions on how to get to the car