What are some good liberal arts backup schools if I am considering schools like Vassar, Bard, and Skidmore?

Well, one of my daughters went to Reed College, the other is at Shimer College. Reed is certainly better known, and my daughter got a very good education there. She recently completed a Master's in Welsh History at University of Cardiff in Wales. She looked at Shimer, but thought it was just too small (130 students). Now she wishes she had gone there. She actually contributes money to Shimer every year, but not to Reed. The one at Shimer skipped her last year of high school (Shimer accepts students before they complete high school) to attend. It is academically very rigorous, but with such a small student body, it's a very close knit community (students, faculty, and staff--even the President knows most of the students). But I wouldn't consider Shimer a "backup" school. It's certainly not for everyone, but about 20-25% of both Reed and Shimer graduates go on to receive doctoral degrees--which is about double the rate of Harvard, Yale, or Princeton, and even higher in relation to Vassar, Skidmore, or Bard. Good luck!