What’s impressive to you about an Honors College?
If you are looking for reputation, then look at U of SC (too late) and Arizona State.
Honors means different things at different places - but note - being in Honors is not going to give you a left for grad school. It will from the point of smaller classes or interesting subjects - but having it on your resume won’t impact grad school nor would it likely impact a job after college. It’s more for experience. There are different levels of Honors Colleges - but look at what they offer.
At Pitt (you’re likely too late for merit) but your SAT would help) - Honors courses are open to anyone…but formal entry into the program is likely harder than the two most consider the top - the two I mention above.
FSU - you’re too late - but it’s another - where Honors is super hard even though it’s not the best known Honors, etc.
In the end, find the right fit - and finances are about fit.
Whether you go to Rutgers or Radford, your med school chances won’t differ - as long as you deliver academically, test wise, and the other areas that are important such as shadowing, etc.
Good luck.