We recently went to Hamilton Pool, which I expected to be more of a pool like Deep Eddy, but I was happily surprised.
It is actually Hamilton Pool Preserve, which is basically a collapsed grotto with a waterfall about an hour or so south of our house. Here you can read more facts, such as the Texas Parks and Wildlife Department noting it as Travis County's most significant natural area.
After a .25 mile (!) hike down some pretty rugged terrain you see a small beach and the pool stretches out from that. I'm not sure how deep it gets, but it is over my head at less than halfway across. Directly across from the beach is a waterfall that apparently never stops flowing, even in times of drought. What enchantment is this?
If you want to take a break from swimming, you can walk around the pool in the rock caverns, and there is a walkway that circles the pool. Pictures can't really do it justice - it's pretty amazing.
Be warned though - I wouldn't advise carrying a bunch of umbrellas, coolers or other stuff. It's quiet a hike down. A tired three-year-old was a pretty good workout!