Austin's fine but it's far from the only game in town. (in state?) You can't skip San Antonio - the Alamo, Riverwalk, catch a Spur's game. I'm not a fisherman, but there are tons of Lakes in the Hill country area - Canyon, Travis, LBJ, and many more. Fort Worth is a cattle town and has many great Steak houses. Then come to Houston for great restaurants, shopping (the Galleria) best downtown skyline in Texas, NASA, the Kemah Boardwalk on Galveston Bay (watch boats, carnival rides, more good restaurants) then head down to Galveston for the Gulf of Mexico. Also Texas is home to thousands of beautiful golf courses if you're into that sport.
It would take a book to list everything there is to do in Texas. Check out a website called Texasoutside.com. I think they rate the Lakes in the state for fishing along with lots of other great info.