Just inquire and remember that San Antonio is a tourist town. Many hotels and motels offer free shuttle service to the airport, local malls, the downtown area and other tourist attractions. Some downtown hotels offer free parking, which can save you money if you are staying more than a couple of days. The Holiday Inn Downtown Market Square is six blocks from the Riverwalk. You can take the trolley to go downtown.
Kids eat and stay free and there is also free parking.
Staying near the airport is a good idea if you're on a budget. If you are traveling with several people or have children, the Hawthorn Suites Six Flags is a good option. From Monday through Thursday, the hotel offers a free breakfast buffet and light dinner buffet. It is close to Six Flags Fiesta Texas and SeaWorld. There are many historical and prestigious hotels downtown to serve the business traveler's needs.