Well, we are partial to the Fort Sam, but you must be military or a guest of military to stay there.
With that being said, our other place is the premium side of the Braunig Lake RV park. It is off of I-37S about 8 or so miles South of the Alamo. It is a Passport America park and our price for premium was $25 a day. If you are not a PA member and want to join, let me know and I'll give you my PA number as a reference.
The non-premium sites are a little crowded. Considering that you will be visiting family, I'm going to assume you just need a place to go for a few hours to get away.