The San Antonio Airport (airport code: SAT) is a medium sized international airport. Once downtown at the Menger Hotel, a rental car would only be needed for sight seeing or visits to SwRI. Suggested transportation options to and from downtown include SATrans Shuttle service (~$10), taxi (~$25), and rental car. The airport is a short ~15-25 minutes travel time to the hotel downtown. Parking at the Menger costs $25/day, but nearby city garages cost $6-8/day. Travel from SAT to downtown by bus takes ~1 hour and requires a transfer.
Map to SwRI