Here are the Texas rules for residency for tuition purposes:
http://www.admissions.txstate.edu/future/residency/residencyrequirements.html
Note that establishing a domicile means significant employment in Texas, buying real estate in Texas, or marrying a Texas resident. It does not mean simply living at the university and going to school there.
With a $30,000 per year parental contribution, your price limits are probably around:
$30,000 per year without direct loans or work: probably some UCs, living frugally
$35,000 per year with either direct loans or work: probably UCs or Minnesota
$40,000 per year with both direct loans and work
Both UT Austin and UIUC are more than $40,000 per year for non-residents.