There are loads of day hikes around Austin, none quite as far as you are asking for, closest hike in is Hill Country State Natural Area near Bandera (link)
http://www.tpwd.state.tx.us/spdest/f.../hill_country/
and Lake Georgetown Good Water trail
http://www.austinexplorer.com/Hiking....asp?HikeID=25
this link leads to other hikes also.