If you're going to engage in a dangerous activity like rock climbing, you might as well do it at a hospital, right?
At Georgetown Hospital, now called St. David's, about 30-45 minutes north of Austin off I-35, there is a nice limestone crag with little polish, stiff grades, and lots of shade. Meet the Riverside Sanctuary.
According to John Hogge's Austin Climbing: Sport Routes, Deep Water Solos, climbing here began in 1993 with loal climber Luke Stollings obtaining permission to establish toprope anchors and routes. Bolting for lead climbing began by the end of the decade.
If you are a Texas climber, please buy and see John's guidebook for more history of this crag; I do not intend to paraphrase or plagiarize him here.
Climbing here is split into three primary activities: sport climbing on the main wall, bouldering, and toproping on the back side of the huge outcrop that faces the main wall. On that back side, though, is one crack that traverses ascends up and left, and it will go on trad gear.
The sport routes have a reputation for stiff grades relative to other Austin-area sport crags. Currently, I can lead 11b sport with an onsight grade of 10b, but I struggled on a 9 and a 10a here.
Exit I-35 at Georgetown and follow signs to the hospital, which you can see from the interstate. Park in public parking around back near physicians' residences and the helipad. Make sure you are in the public spaces; do not jeopardize access!
In case the outdoor public parking is full, you can park in a garage (not sure of there is a fee because I have never parked there).
Walk past the residences and find a gate with trail access, posted regulations, and waivers to complete. Fill out the waiver; again; don't jeopardize access! Take the short, steep trail down.
At the main wall, there are several bolted routes ranging from 5.9 to 5.12c. The grades are from John Hogges's book and may not match the MP grades. The routes have from two to four bolts each and chains for anchors; a 40m rope will cover anything here.
Facing the main wall is a huge outcrop that has several bouldering problems (and others are nearby). Please see the MP page and/or Hogges's book for details about bouldering.
On the back side of that outcrop is a slab, and atop it are several easily accessible pairs of bolts for building toprope anchors. According to the guidebook, the routes range from 5.6 to 5.9, though I felt they were more like 5.4 to 5.7. Nothing felt close to as hard as the 5.9 or 5.10a I led on the main wall, but it's always subjective.
Splitting a good chunk of that back side is a lovely crack that will go on trad gear. On MP, it has a V0- grade; I would call it 5.4. A good tree at the top makes a convenient belay anchor.