Most people will fly into San Antonio. However, if you plan on renting a car anyway, you might also check flights into/out of Austin. The Austin airport is a quick 1-hour drive from San Antonio and may result in cheaper airfare depending on your location.
DO NOT WAIT TO BOOK. This weekend is the opening of Fiesta, a huge 2-week citywide event so rooms will fill up fast. While we did reserve this small hotel block, there are numerous hotels in all price ranges a short distance from the church and reception venue guests may choose from. There is no central hotel where the wedding party will be staying. We recommend booking a hotel near either 1) the airport, or 2) downtown/Riverwalk. Both areas are roughly 10 minutes away from wedding events and convenient to pretty much everything.
All major car rental companies serve the airport. The city is also served by taxis, Uber, and Lyft.