I hope your student knows your financial constraints. There are some great private and public schools that aren’t huge, and might come in under your price point. Miami of Ohio is one. New College in FL is another. Both fine schools. Other places she should consider…Arizona, New Mexico, UT Dallas, Denison, Union (they just reduced their tuition, IIRC). For the public universities, have her apply to the honors college which is one way to make the large school shrink. If she is willing to do public honors colleges, Alabama could be in the mix as well.
I happen to love Pitt, and think it would be a good option…but to get the best merit aid, you have to be a tippy top applicant applying as early in the admissions cycle as possible.
And that is why you chase merit. There are lots of families who can’t pay what the net price calculator says they should be paying. Merit aid is your friend. And it’s not the colleges buying rich kids…it’s the colleges buying highly qualified kids.
One thing you need to know…in the vast majority of cases, merit aid is awarded by admissions based on the strength of the student application. And in most cases admissions has no idea what your finances are.
Need based aid is awarded by the financial aid office. Those are the folks who know your finances.
I would suggest you run the net price calculators as soon as possible. Keep in mind that in January, they will be set up for kids enrolling fall 2020, which is a year prior to when your kid starts. Financial aid policies DO change so you will need to run the NPCs again in September 2020 for a better idea for when your kid is starting.
ETA…would she be interested in any of the women’s colleges in the northeast? Some of them give merit aid, and are excellent colleges.