I also like history, so find the Alamo and missions interesting. I’ve also enjoyed the Capitol tour. But I did those long ago and haven’t recently repeated, though I’ve visited Texas many times over the years.
BTW, Waco is within your parameters, but it’s not to everyone’s taste. Worth considering. Personally, I like whiskey/whisky, so enjoy stuff like this: Balcones Distillery - Stay in Waco.
@HelloOutThere you must visit Rainey Street whilst you are in Austin. Hubby & I love it there, it’s a hub of wonderful bars, restaurants and entertainment
We enjoyed playing outside Jenga when we last visited!
You can go to the Whole Foods flagship store. And see Lake Travis, it’s just gorgeous, reiminiscent of the California coast. My husband’s cousin, an Austin native, took me to a restaurant overlooking the lake, it might have been Oasis. Loved it. Thanks to a THS sit, I got to see Austin.
Be sure to stroll around Town Lake AKA Lady Bird Lake trail. Mt Bonnell has a great view.
Museums: The Blanton and the Bullock History Museum can be done the same day. There’s also the LBJ library and museum. Umlauf Sculpture garden, Zilker park and a peek at Barton Springs pool can all be done in an outing. The diehards will be swimming, but much too cold for me!!
I don’t think you will see bats this time of year. If you have some grocery shopping to do, check out Central Market.
Have some tacos! There’s plenty of brewpubs and a variety of good food in Austin.
For an out of town adventure, consider Inks Lake State Park and Longhorn Caverns. Closer in, Pedernales State Park.
Broken Spoke for dancing. Mount Bonnell for the view. Congress street bridge for bats. Dovetail Tattoo if you are looking for ink. Elephant room for jazz. Zilker Park for open space. Lady Bird Johnson Wildflower Center (Austin’s Kew Gardens!). Mother’s for vegetarian and old-school hippie vibe. Amy’s for ice cream. McKinney Falls State Park for hiking. Pretty much anywhere for tacos and beer. All of that is in or near Austin. You can catch a wine tour into the hill country. The wine’s just OK but the scenery is awesome. In under four hours you could get to beautiful San Antonio, the beaches of Corpus Christi, Dallas (yawn), my home town of Houston (ick), or 'bout half way to El Paso. But in 4 hours you can’t get out of Texas in any direction. Maybe check out Bandera if you want to drive a bit. Cowboy Capital of the World. But Whacko? Not sure why so many people recommend it. Unless you like sitting in your car watching eternal freeway construction. Or can catch a Baylor game. But they don’t play in January.