Welcome to WildTexas.com, Johnny! Prepare for a bit of "information overload" here...
Mosquitoes are going to be a challenge everywhere, though especially present at places with a lot of surface moisture like
Brazos Bend SP, as you mentioned.
Have you considered
Bastrop State Park? The
Texas Mileage Guide puts it at just 125.9 miles from Conroe, Texas. The park's notable for its dense pine forest -- a relict portion of forest separated from the East Texas forests. Great hiking trails, lots of shade, campsites and cabins, even a golf course! The plus is
Buescher State Park is nearby, linked to Bastrop by a forested road. You could camp at Buescher if you prefer, it's less developed than Bastrop and has some great picnic areas. I'm not guaranteeing the mosquitoes haven't figured out that there are warm, juicy hikers beneath the dense pine tree canopy, mind you.
I'd avoid the area coastal parks and gorgeous
Palmetto State Park near Gonzales for the same reason you're avoiding Brazos Bend --
skeeters. That said, there is something a little humbling about visiting parks where you're guranteed to donate blood to the local skeeter community... in parks like
Aransas National Wildlife Refuge and Anahuac NWR, the skeeters literally attack your vehicle's windows, having learned there's LUNCH inside!
---
It's a bit out of your 1-3 hour driving range, but there's also the two units (Calliham & South Shore -- Calliham's more developed) of
Choke Canyon State Park. The Texas mileage guide puts it at 235.8 miles from Conroe, Texas. Heavily developed but large park with exceptional wildlife viewing (the deer there are quite tame, and it's not uncommon for traffic to stop on a park road while deer, wild turkey and javelina feed!)