Well I dont think there are any challenging hikes around Austin unless you count doing them in the summer when its 105 out. Enchanted Rock is nice and can be a challenge its a pretty steep up hill hike if you are out of shape. Lots of trails around the rock as well.
Several people hike out at bull creek. or Mckinney falls. Check out meetup dot com there are a couple of hiking groups that do things around Austin and the State good way to learn about some of the places.
The trail at Enchanted Rock is pretty short, but climbing to the top of Enchanted Rock is something you have to do. Pedernales State Park has some good trails.
Bastrop State Park was fun to hike until the wildfires hit two years ago. I have not been there since. One may still be able to find a good hike or two there.
Guadalupe Mountains National Park in West Texas has some great trails. It is a bit far away, but if you can do an overnight or two is worth it.
Hiking in Austin? It's more like outdoor walking. Wild Basin has a nice hike. Two trails, one short probably about 1/2 mile while the path less travel is more challenging and is a little over a mile long. Of course if you want real hiking then head up to Colorado during the summer. Hike up one of their many 14'er and you'll see how easy it is to 'hike' in Austin - literally a walk in the park.