@TrendaLeigh I would recommend visiting during the school year if you can, just to see the campus in full swing. If summer is the only time, I think that would be ok, but you might not get to see some things (for example, we had a good time seeing the extracurricular Baja racing and Mars robot design teams, but I don’t know if they are active over the summer.)
For your visit, get in touch with the Honors College, and they can plan a good visit itinerary for you. When we visited, my son worked with our regional admissions officer (here in Colorado) rather than the Honors College directly, so I think either way would work. Let them know the NMSF probability, so they can include info on the NM scholarship. Also, if there are particular programs your daughter is interested in be sure to let them know that too. We talked to people about Randall Research Scholars and Blount Scholars, and my son liked what he heard enough to apply (and be accepted!) to both. On our visit he also had a chance to sit in on a class, tour the engineering facility, talk to professors and see the chem labs.
As far as Randall Research Scholars goes, I don’t think your daughter needs a higher SAT–that’s a great score! Prior to applying, the advice my son got was to really pay attention to the essay–it is not enough to have high test scores, NMF, AP (IB) classes because almost everyone applying will have that–those things won’t set you apart. If I recall correctly, the essay asks why you would be a good fit for the program, but also why the program would be a good fit for you. I think researching the program and having compelling answers to these questions is what will set you apart. Be sure to pay attention to the application deadline–it was earlier than a lot of the other deadlines my son had.
I would totally have your daughter try the ACT. Both of my kids have thought it was easier than the SAT, and it seems easier to get a perfect score. UA gives the Presidential Elite scholarship for a perfect score (ACT OR SAT) which is a nice backup to have in case national merit scholarship doesn’t work out.
Good luck!