you're not confined to becoming a professor at a state school. This is a legitimate fear
Most extremely smart academia-bound computer scientists consider that a dream, not a fear. Realize that many state schools are in the top bunch (e.g. 20 or 30) in the US. Unless by "state school" you mean "shitty state school." Like, "X State" where X is not actually a U.S. state (no offense, but those annoy me).
For a professor, the main difference in quality of the school you work at is the quality of your students. This matters a lot, research-wise, because most profs that do a lot of top-quality research farm it out to their grad students. e.g. with 8 good students, you can increase your productivity about 8x.