I have hesitated to weigh in on this one. The teacher's expectations, all desirable, are hard to meet in Texas in the summer. It is pretty much hot, dry (especially this year), and muggy. For this area (as I am sure you well know) our "three seasons" are fall, winter, and spring!
Enchanted Rock is awesome but this time of year will be hot with no water to jump into to cool off.
Pretty much all of central Texas' public land is more "front-country" with established campsites even in the backpacking areas. One suggestion I have is to go to Pedernales Falls State Park, and hike in to Wolf Mountain Primitive Area not on the regular trail (2 miles of ranch truck doubletrack) but on the "Horse Trail." This is not on the park map but the park office will give you a map. You have to bushwhack a little ways up the slope to get to it from the trailhead parking. The Primitive Camping Area is on a bluff above the river. It is pretty well used, but not with fire rings and tent pads and stuff, just woods. No fires. And you can go down the bluff and hang out in the river when it's hot. The Pedernales River at that point is not deep enough for boating, though.
Lake Georgetown has a 16-mile hiking loop around the lake that you could hike part of and boat part of. But it has established campsites, some of which are accessible by road. Lost Maples near Vanderpool has a 9-mile loop that has a much more backcountry feel to it, and a couple of ponds where you can get in the water, but the camp areas are designated, and there isn't anything you could boat in.
To cool off in the summer in Texas you need either to be in the water or the high country. About the only country high enough and cool enough to be comfortable this time of year is Guadalupe Mountains National Park, and that is definitely more than 6 hours away. We are taking a group there next week. No water. Designated backcountry sites. But definitely roughing it, if you backpack. We are day-hiking Guadalupe Peak and then going on a 2-night backpack loop through The Bowl and McKittrick Ridge. Not, however, a beginner's trip, what with carrying water. But spectacular country.
Southern New Mexico is a good bet, but much farther away. I am not familiar with the north Texas destinations like the aforementioned upstream on the Brazos, you might want to look into that. Or you could plan on paddling one of the navigable central Texas rivers (upper Guadalupe or lower Colorado, for example). We took a couple of spring break trips a few years ago on the lower Colorado, and although it goes through settled country and private land, it is beautiful. Like a thin film of wilderness along the river, with wildlife and tangled brush and shifting sands and gravels, big overhanging trees. You camp on the islands and bars in the river channel. LCRA publishes a map booklet. We did Big Webberville to Smithville one year, and Smithville to Columbus another. Nice!
Have a wonderful trip, wherever you go!