By Googling "Hotels Near University of Texas Austin", I found this website listing many hotels of varying prices which are near UT. I'm not recommending that you book through this site, but it gives you some useful information. http://hotelguides.com/colleges/texas/university-texas-austin.html

Being within walking distance of campus is helpful so that you don't have to pay for parking in one of the campus parking garages. But if you don't mind doing that, I guess I would recommend staying near Lady Bird Lake and downtown. When we go to Austin, we like the Embassy Suites Downtown. It's got easy access to the hike-and-bike trail around the lake; you can walk down Congress Avenue and see all the funky shops and food trucks; and it's near 6th Street, although you may not want to take your high school junior there quite yet

Agree. Hotel near the lake would be best to enjoy the City. And finding a parking spot somewhat close to campus is not too difficult. Embassy Suites, right on Congress and the lake, is one of our favorite places, but many others around the convention center area are also great, being just 4 blocks or so from the lake and 2 blocks or so from the famous 6th Street area. When family is with us, we like staying at the Doubletree Suites on Guadalupe at about 12th Street, which is about 7 blocks from the campus and 12 from the lake. All of them are right off of Congress Ave., the main street of downtown and the street that leads up to the Capitol.

Thank you!