I’ve heard that the U. of Arkansas is a good place for bikers. The area (especially Bentonville) is really designed for bikers, including lots of mountain biking.
Universities in New Orleans would work well for these purposes (Tulane, Loyola, Xavier, Dillard, U. of New Orleans). The terrain is pretty flat and New Orleans is a silver-level community for biking. There are an increasing number of bike lanes on the roads, and there is a nice bike path along the lake as well as a long bike trail along the Mississippi River.
Speaking of the Biking Friendly Communities, there is this database that awards communities (and universities) as well as states. Even if a university is not designated, if it’s in a bike-friendly community or state, that would certainly help to find choices.
There’s also the Hilly Hundred for interested bike riders.