A program that is fairly unique is Ohio Universities Honors Tutorial College. It is patterned after the tutorial colleges at Oxford and Cambridge in England. It is pretty selective approximately 300-350 qualified students apply each year and they accept around 80 or so with around 75-80% accepting. It comes with a pretty good scholarship. Ohio U is a beautiful campus. Here is some info.
@chris3499 UVM actually is very generous with merit-based aid to OOS students. A friend of mine with a 3.5 GPA and an 1900 SAT was accepted to the honors college and received 15K/year in merit. OP’s daughter would likely get a lot more. They stack scholarships and will give an additional 10K/year if the prospective student was a national merit finalist or semifinalist. It was actually cheaper than Umass Amherst (my instate flagship) for several students in my school. Not sure about need-based fin aid.
Burlington is a great town.
@Qwerty568 thanks for the info 
Hmmm, the honors programs at bigger universities are sounding very promising. She just found out yesterday she is recognized for the National Merit Scholarship program. No idea yet if it is just a commendation or as a semifinalist. Looks like we have some research to do. However, as I said, her GPA is 94. I understand that honors programs often want a higher GPA.
Try Arizona State…the school has a repuration of being a bit of a party school (per my kids), but our friend looked at their honors college and was so impressed he almost turned down UCLA for it. It is a self contained honors program and is highly regarded. You live, eat and take classes with honors students and when you want the “real college” experience, you can participate at ASU (like football games). HAven’t been myself, but have heard great things.
I’m not sure what you mean by this, but it sounds like you may be saying Barrett is a free-standing college offering all the classes students need for a degree and offering its own majors. It’s not.
While they do offer some upper-division honors classes, and while there are some special sections of upper-division classes in the regular U designated honors, the plain fact is that most if not all of the classes a Barrett student takes outside of the 36 hours required to be honors will be regular classes in the regular university.
A 94 is roughly a 3.75 so you’re fine for all Honors Programs that I know of (and most don’t have an absolute, cut and dry GPA threshold even if they like that level).
I didn’t like UVT’s Honors college much - there’s only one class per semester that’s Honors, as far as I could tell. At some universities, you can take 3 or 4 of your 5 classes per semester your first year in the Honors College. I do like UVT and Burlington though.
Thanks everyone. These suggestions are a great starting point.