My wife and I just got back from 11 days in that area. stayed at an RV camp on the Guadalupe River near New Braunfels. As mentioned above Gruene (pronounced Green) is a neat small town with good restaurants, shopping and live music venues.
The Texas Hill Country has many very good wineries and we spent a day touring these. Look at
Plan Your Trip to the Hill Country | Texas Hill Country Wineries for trip planning. Our favorites were Pedernales Wine Cellars with live music on the patio overlooking a great view of the hill country, and Grape Creek Winery for lunch.
There are also very good distilleries, including Rebecca Creek and San Luis Spirits (Dripping Springs); very friendly staff at both of these. Visit
5 Distilleries to Visit in the Texas Hill Country for a High-Spirited Tour for planning.
The hill country is also home to olive orchards if wine and spirits aren't your thing. Texas Hill Country Olive Orchard is near the Dripping Springs distillery and also a good stop for lunch. Visit
https://texashillcountryoliveco.com/ for planning.
Finally, try some kolaches when in the area. It's fun just scoping out bakeries that serve sausage and cheese kolaches for your morning coffee. A good place when in the Austin area is Round Rock Donuts
ROUND ROCK DONUTS Try their famous yellow donuts.
Other than that, my suggestion is to get out and drive - there's a lot of fun to be had just exploring.