We use Budget, also. They're right near the pier and have a complimentary shuttle.
We like to rent a car when arriving a day earlier so we can visit our corporate office, friends, or cruise line offices and Budget is the closest and the cheapest.
Travel Agent/Cruise Specialist w/13 yrs exp and 48 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!