Just taking the back roads from Sam Houston SP in LA to Lost Maples W of San Antonio and was looking for something roughly 1/2 way. If Google map is to be believed, it's 80 minutes longer then I-10.
If you disable highways on Google map you might see the three suggested routes it shows me, all north of I-10.
Somerville lake seems to be pretty central, I see a couple COE parks as well as the state park so there should be plenty to pick from.
On 2nd look, one of the COE CG's as well as Somerville SP are closed, must have had some mean rain down that way.