Burnet is a friendly Texas Hill Country county seat of roughly 6,400 people with a walkable historic square, easy access to the Highland Lakes, Longhorn Cavern and Inks Lake State Park—perfect for multiweek stays if you want outdoor recreation, local cafés and a low-key, community feel.
Weekend options are close by: Marble Falls (about 13 miles) offers lakeside dining, breweries and water activities, and Austin (≈50 miles) gives full-city nightlife, concerts and an airport—so you can enjoy quiet weeks and lively weekends without feeling stuck.