There a LOTS of places to hike around Austin. Not many long hikes, so one week will be a collection of day hikes.
I think I stayed at Emma Long Park before; this will be my base of operations for the week.
Emma Long Park has the (2) Turkey Creek Trail (approx. 2.75 miles) and Lake Line Trail.
It’s a short distance from there to the (4) River Place Nature Trails, (8) St. Edwards Park, and the (3) Wild Basin Wilderness Preserve.
A day at each of those and then back home.
Other visits could include:
(1) The Barton Creek Greenbelt
(7) Walnut Creek Park – Multiple trails; could spend a couple of days here
Mr. Skipper 