Moving to San Antonio - would love some info

Hi. We just found out we are moving to San Antonio from DC and are really excited about our new adventure. We have been down there for business and leisure but dont know much about the area. My husband will work at Lackland Air Force Base and therefore we want to live as close as we can but in the best area possible. We want to rent a nice house (around $2,000 per month max) in a really safe area and with great Elementary Schools. Can someone tell me if we should live in San Antonio or if it is best to live in a smaller city just outside it. If so, what are the areas. We want to be as close as possible to the base. Neighborhood info or zip codes or just "eastside/west side" would be super. Thanks for your help and happy holidays!!