Where would depend heavily on the weather forecast. As you well know during that period in Texas it may be cold and rainy or icy, or it may be sunny and 75-80 degrees wearing shorts and T shirts. That would make difference on whether to head north, east, south, or west.
Lots of different type areas with regular private RV parks and/or state/COE type parks that would be good with outdoor activities if the weather were favorable.
We like to go to
Kerrville Schreiner Park in Kerrville to get away from a typical side by side RV park. Formerly a state park now run by the city. Large (over 500 acres) with relatively few RV sites leaves lots of room for nature. Hiking and biking on paved roads and also maintained off road hiking/biking trails. Deer routinely come grazing thru your RV site. Split by the highway, the river side is along side the Guadalupe River where you can fish/swim/sit beside the river. We prefer the hill side which is the much larger part where the hiking/biking trails are located. But best enjoyed during nice weather.
And Kerrville is a nice city to visit if you have not been there. Close to other interesting hill country towns such as Fredericksburg, Comfort, Boerne, etc.
