San Antonio is famous for the Alamo, but the city also has four other Spanish missions, all in much less urban settings south of the Alamo and downtown San Antonio.
You can certainly drive between all four of the missions - Concepcion, San Jose, San Juan, and Espada, but you can just as easily bike between them.
The Mission trail is about a 15 mile round trip if you do all four missions - if you want to make it shorter for a family trip, cut out Mission Concepcion, because that mission requires some bike lanes on city streets.