You really need to find out why she doesn't want to apply to any other schools. If it is the money, she needs to understand that she may in fact be better off at one of the private schools. I don't have a link, but I recently read an article listing the top 10 schools in terms of meeting aid. Princeton was the top school, with the average graduate leaving with an average of less than $10,000 of debt.
If it's because of pressure from her peers, you may need to turn her own words back to her. She is the one going to college - not her friends (they are, but her experience will not be theirs). At a big state school, she is less likely to have any classes with them, and they are likely to grow apart. My DD is a junior, as we have been visiting the local college open houses, to get a feel for different types of schools (though she already has her own short list). She has already decided she will apply to one of the state schools as a safety school, but will only attend if she gets into the honors program, and can live in the honors dorm. Yes, she will already be spending her days with those same students, but she knows a regular dorm could be a distraction to her.
I would encourage her to apply to at least one of the "reach" schools, and hold off on the final decision. She has her acceptance at the state school, and that option will remain open, unless she participated in an early decision program. It's better to keep her options open, and let her know that the final decision is hers - just make sure it is a truly informed decision. The only way I would allow my DD to apply to just one school is if she fell in love with that school and was accepted early.
I found the article, or one like it: 10 top colleges with lowest graduating debt
http://portal.kiplinger.com/slideshow/lowest-debt-private-colleges/7.html#top