All of the universities you listed are excellent for Classics. I’ll admit I am somewhat biased since I received a degree from one of the universities and took many courses at another.
Michigan and UCLA, along with Berkeley, are unique among public universities in offering not only Classics but also adjacent fields such as Egyptology, Assyriology, and (in the case of UCLA) Indo-European linguistics. Michigan also has the Kelsey Museum of Archaeology and a large collection of papyri, mostly from its excavations at Karanis. UCLA benefits greatly from its close associations with the Getty Villa, one of the finest collections of ancient art in the world.
https://lsa.umich.edu/kelsey
https://www.getty.edu/visit/villa/
UT Austin and Cincinnati have pretty well-rounded Classics programs, but historically they have been especially strong in Bronze Age archaeology and Linear B studies, for which there’s nowhere better except Oxford. UT Austin offers more in the way of related disciplines; it is strong in archaeology, particularly Mesoamerican studies, and it has some excellent Semiticists on faculty like Na’ama Pat-El.
UNC Chapel Hill is relatively unique in guaranteeing financial aid to all admitted domestic students. As far as I am aware, UVA is the only other public university to make that pledge, although Michigan has been improving its financial aid. Carolina has a very good, well-rounded Classics program, and the town of Chapel Hill itself is lovely. The religion department is extremely strong at Carolina as well, with some very high profile faculty like Bart Ehrman and Jodi Magness.
A few others to consider – Ohio State, Wisconsin, U Minnesota, U Iowa, Indiana U, SUNY Buffalo, U Arizona, Florida State, U Missouri, CU Boulder, UT Knoxville, and probably others that I’m forgetting.
There’s a lot of good undergraduate Classics programs out there, and only applicants to PhD programs need to be concerned with looking for the best programs in the field. Any university that offers introductory and intermediate Greek and Latin every year should be enough for your purposes, especially if you’re not coming in at a high level in Greek or Latin.
Notre Dame has a more or less comprehensive list of Classics departments, and the SCS has a good albeit not complete list of Classics programs at universities.
https://classics.nd.edu/about/resources/classics-around-the-world/
https://classicalstudies.org/education/graduate-programs-north-america