For a nice leisurely ride, take River Road from Canyon Lake to New Braunfels on a weekday Morning. Eat some sausage, drink some German beer, go back. It's mostly in the shade, which helps. The roads to Canyon Lake can be fun too.
Anything around Luckenbach is fun too. Also, go out 71W to Bee Cave. Turn on RR 3238 (Hamilton Pool Road) and just keep going to Hamilton Pool. It'll turn into 962E, or there are any number of side roads that'll get you to 281 or back to 71W. They are all fun.
Have you been on Lime Creek? It runs between Volente and Anderson Mill which ultimately crosses into 1431. 1431 is fun too (not as much as it used to be a couple of decades ago
There are a number of interesting roads going towards 29.
If you want to venture further, go in the direction of Bandera, Utopia, Garner State Park, etc.
Devils Backbone which is also the hill country area around Wimberly is a must!