The missions were built in the 18th century by the Spanish, the missions were a way to expand into their country by converting local Indians. The Missions were a reminder of church and state, since they did not have a separation of the two. There are five Missions in San Antonio with in the national parks site. You do have to drive to each of them. Seeing the missions could take a day or longer if you wanted to do tours at each and really walk all the grounds.
The Alamo is of course the most famous of all the missions in San Antonio. And is the easiest to see since it's down town. However in my opinion it is not the prettiest or most interesting. Plus you have to put up with a TON of other tourists. As you travel the missions route there is fewer and fewer tourists at each one. I would encourage everyone to visit all the missions, even if it is just to run in and take pictures. They are beautiful.