Because her stats are so high, she might get some outside scholarships from Women in Engineering or some of the civic groups (Elks, DAR).
If she is a NMF, I can’t believe anyone has not mentioned the exceedingly generous scholarship offered by Alabama. You might also want to look at Auburn. If you can qualify for in-state tuition, then Texas A&M and Texas are both excellent engineering schools. If you are in-state in Arizona, then ASU with the Barrett Honors School is an excellet choice.
@Peruna1998 Thank you for the suggestions. Right now the NMF schools we are considering are UF, UCF, UTDallas, and ASU/UofA.
The discussion on the relative value of an expensive elite vs. free or almost free engineering degree is being weighed heavily at this point. We will try to visit the NMF schools above (and maybe Alabama) to get a feel for the campuses and see what she thinks. She is having a hard time imagining herself in the south/TX but that might be a luxury we cannot afford. Hoping a visit will spark some interest. Or she can stay here in AZ and do great. We are really grateful in that there are no bad outcomes - just need to get the teen on board 
@jilywily If you visit Bama, I recommend making arrangements through the honors college and make an appt with Dr. Sharpe. You might also have your dd look into RRS. It is a specialized honors program focused on research. There have been students in RRS (formerly known as CBH) who have been Goldwater scholars every yr for the past decade (???) not sure exactly, but quite a few. This is a link to this past yr’s winners. https://www.ua.edu/news/2017/04/four-ua-students-named-goldwater-scholars-in-2017/
@jilywily I just read the UF NMF thread. Have you read the details closely? UF is not guaranteeing the scholarship will be available all 4 yrs. It really is at the mercy of the legislature; http://talk.qa.collegeconfidential.com/national-merit-scholarships/2099031-florida-nmf-scholarship-for-out-of-state-p1.html This post was especially informative: http://talk.qa.collegeconfidential.com/discussion/comment/21710622/#Comment_21710622
FL was not offering OOS scholarships when my kids were applying, but the scenario at UF does need to be entered into with full understanding of what is being offered. It does not sound like there would be any issue with UCF.
NMF will automatically get your student the Patterson Scholarship at University of Kentucky in Lexington.
Four years of full tuition, plus $10K for on-campus housing/meal plan freshman & sophomore year. 3.0 to maintain the scholarship.
We have a junior at UK on the Patterson. Although initially not liking the school (she thought she was forced to go there, and she’s kinda right about that), she is very happy now. She didn’t even come home for the summer!
She is not in engineering, but fell into a group of friends who are in engineering. She reports her friends are very happy too, and have had amazing internships.
Our family likes Lexington a lot. We can get direct flights to and from Chicago. It’s a college town, but also a large, but not too large city. Basketball season is super fun. Lots of great hiking available just a short drive away. Good bus system. UK has been investing a LOT of money in new dorms, new student center, new academic buildings, and a new Honors College.
Worth a look!
I second the earlier suggestion to have a look at RIT. Lots of art there as well as engineering and they have been very generous with merit money for high stat female applicants.
Did your daughter nix colleges in states like Oklahoma before or after visiting them? I recently drove through the southwest with my kid who recently graduated from one of the top-15 schools that your daughter is probably interested in. Kid’s jaw dropped when we looked at Oklahoma State. Dropped farther at U of Oklahoma.
Granted, neither school will stop conversation at a Long Island cocktail party, but each is stunningly pretty, scrupulously maintained, friendly as could be, and adjacent to a lively business district.
http://www.ou.edu/admissions/nationalscholars/national-merit-scholarship
@Mom2aphysicsgeek Thanks for the tip re: Benaquisto at UF having potential risks that we will have to add to the
mix.
@Midwest67 @moooop Kentucky and Oklahoma - Not visited and never been to either state. I admit to being western mountain people with an unwarranted aversion to the midwest. We really should look.
I have been also investigating engineering curriculum that is “innovative” or design based with project based learning opportunities throughout the 4 years (that we can afford). So not MIT, Harvey Mudd, etc. A couple of schools that came to my attention that might be in that category are Rowan University and USCarolina. A couple people have already mentioned USCarolina as a general good choice. Any thoughts on these programs or other for “innovative” design thinking approach?
CSU-SLO is very hands-on, project based, but don’t know how the non-STEM programs are, Stanford is still your best bet given your criteria, obviously you need backups, SLO could be a possibility. Good luck!
Does Stanford fit the budget criteria?
A “standard” engineering curriculum can also be very “hands-on”. Look into what type of design teams are available at these schools. The larger programs tend to have dozens of well funded design teams.
For example, my DS17 (Aerospace) is part of the Gator Motorsports team. He’ll spend 3 to 5 nights a week working in the shop, helping to design and fabricate the car. He’ll also plans on spending about 2/3 of his winter break and most of spring break staying on campus to finishing the car. They can be very time consuming, but you learn a lot/u.
http://www.gatormotorsports.com/
Consider what student groups/clubs/undergraduate research/design teams are available. She shouldn’t limit herself to taking classes. She’ll have a lot more fun, and will have something interesting to add to her resume.
It’s not that you can’t find both at most colleges, it’s just that here in CA, the CSUs are more hands on while the UCs tend to more theory, which is based on feedback from students or parents who have kids at both places and compare.