Native Texan here, Austinite for 20 years, then lived in a bunch of little towns east and west of Austin in the 18 years since. You've gotten good advice here.
I did want to bring up two things: price, and cedar fever. Desire for Hill Country living has exploded, and you will pay much more for a home there than one on the Houston side of the Balcones Fault. Cedar fever that attacks Austinites every winter is hard on a body (allergy to blooming juniper trees that are everywhere). So you might have to boost your Claritin budget!
That said, for Hill Country rural, I recommend Burnet, Marble Falls and anything along the Highland Lakes chain (Lake Buchanan, Inks Lake, etc. thru to Austin), excepting Granite Shoals. Also lovely are the towns around Boerne/Bandera/Medina. Fredericksburg is awesome, as are Llano and Blanco.
However, once you cross the fault, your trip to the beach grows quite a bit, simply due to congestion surrounding I-35. It's four hours from Austin to Port Aransas (nearest beach), more like six from somewhere like Burnet or Bandera.
Over time, I've grown fond of towns east of Austin, like Giddings, Elgin, Brenham, La Grange, Smithville. They are still more "country" than the more gentrified Hill Country towns. But that's purely a personal preference.
Have fun pondering the possibilities!