Everybody adapts to their environment, and in Texas, that means swimming when it's hot. As long as we get rain, the swimming holes are just absolutely fantastic. One summer, I went 3 or 4 times a week. Pack a bag with a few beers, bike to a trail, hike down to the water. The hotter, the better. You get super sweaty on the trek down, but getting in the water is so. damn. refreshing.
However, if you like hiking, Austin really sucks compared to Seattle. Washington has soooo many great hikes in close proximity to Seattle (less than 2hr). The best hikes around Austin feel like nerf trekking. Your best option is to drive 6 hours to Big Bend. Some folks recommend Pedernales or Enchanted Rock, but both are very popular and not at all challenging.
I love Austin, but dammit, we don't have mountains.