I think you’re getting a lot of good advice here. Some things I want to emphasize or suggest:
Definitely get Fiske. This will help her get a sense of the students and the culture at each school and give her some sense of where she’ll fit in and be happy.
Has she looked at Wesleyan? It’s another reach, but an AA SJW who wants a non-urban LAC in the NE and whose grades are much better than her SAT should at least give it a look. Test optional, lots of diversity of all kinds, meets all demonstrated need, enough SJW’s for almost anyone, smart, interesting people.
If she’s willing to consider women’s schools, with their higher admit rates, she should take a look at Bryn Mawr. They have an incredibly tight relationship with co-ed Haverford; they fall just a little short of being one combined school. She can take classes, live in dorms, join clubs and eat in dining halls with men.
Just a reminder that everyone’s list should have reaches, matches and safeties, all of which you can afford. Those are hard to quantify exactly, but if you poke around here on CC and on the internet generally you should find some useful definitions. If she’s an auto-admit to UT and would be willing to go if she didn’t get in anywhere else, then that’s a great safety. The she can add 1 or 2 safeties that aren’t as safe as auto-admits, but that are still quite safe. Austin isn’t the NE or NYC specifically, but it’s not like the rest of Texas, either.
Her matches and safeties are a great opportunity to pursue merit aid. If there’s a significant difference between what the schools think you and her father can afford and the reality, you want merit aid. She will get that at schools that give merit aid (not all do) and that want to woo her because she’s at the top of their stats. That DOESN’T mean so-so schools or students.
I don’t know exactly how the NYS residency rules work, but based on the language people have linked to and my general sense of how states approach the issue for college students, I would not assume that college vacations with her father would constitute “living with him.” I don’t find it inconceivable that it could mean actually living with the parent full time and commuting to school. Again, I don’t know, but I’d check very carefully before you rely on it.
I’m not persuaded that Binghamton is a safety. They consider standardized test scores very important and their mid 50% ranges are M:650-720, CR:640-711. For the school to be a safety, especially with your daughter applying as an OOS resident and with only a 40% admit rate, I think her scores would need to place her in the top 25%.