The State Park is about 1 hour and 15 minutes away from Austin, TX, which is the closest major city and airport. It is about 4 hours from DFW, which we know is where much of our family will be travelling from. We highly recommend getting a hotel for the night, unless you are an Austin local and do not plan on drinking.
The State Park is in between Johnson City and Fredericksburg. Johnson City is a little closer and cheaper (15 minute drive) but smaller, and Fredericksburg is larger with more stuff to do but further away (22 minute drive) and more expensive. If you are wanting to make a little vacation out of this trip, we recommend staying in or near Fredericksburg for the whole weekend and enjoying some of the fun shops and German culture.
We also recommend checking out Airbnbs and Vrbos because they are sometimes cheaper! (The underlined words are links)
You could also stay in the Austin area, as there will be plenty of time to drive from Austin to the park.