There is an Embassy Suites downtown, which would be about 10 miles away from Lackland. On an award stay, you could get 2 Queen + sofabed, which would accommodate five people (albeit a bit crowded). I might just spring for two rooms, though. Graduation from basic training would be worth it!^

Although downtown is a bit farther than you might want to be, at least there will be restaurants, the Alamo, the Riverwalk, and the Rivercenter Mall down there.