In general unless there is an enforced burn ban there are a number of hike in parks reviewed on this site where you can have a fire. Here is a link to the state parks, some in the area you asked about.
TPWD: Campsites
potable water might be a different for example hill country sna notes
Be sure to bring drinking water; Potable water is not available;
All water must be treated.
Camp fires permitted in fire rings only, except during burn bans.
TPWD: Hill Country State Natural Area
just read through the parks on this site and on the state parks site:yes: