Washington-On-The-Brazos, TX

I think I would do Lake Livingston. Depends on how you want to leave LA, but you could go north and catch 190 and run that west to Livingston. Then 21 or 290 west to Lost Maples.
The bridge on 190 over Steinhagen Lake will scare you regarding clearance, but I always made it! I think it shows 14 ft clearance.

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.

Sommerville is certainly closer.

If you want to visit that park the nearest RV parks are up TX 6 towards College Station.

Thanks folks. Just tried the TX SP Reservation web site again after reading the above, all it shows is non camping items. I must have confused it this morning as I looked at many state parks one after the other. I'll use either Somerville or Livingston.

Nearest State Park with camping would be Lake Somerville, about 45 or 50 miles depending on the route you take.
Right now, all campsites are closed due to flood damage, but scheduled to reopen in January. SOMERVILLE

It's a historical park. There's no camping other than a few spots for hosts.

I've been there, and I did not see any campground. This is a historical park as you mentioned. I think what they are referring to regarding reservations is reserving one of the group gathering facilities which there are several.