Hi /fellow travellers

Sorry, in advance for the long post!

I hope this subreddit is appropriate for my post. As the title says, Ill be living in the United States for a few months next year as part of a studying abroad exchange through my uni. Im hoping that people who currently live in the US, or have lived there in the recent past, can help me choose the most suitable state/city for me based on what Im looking for in terms of a (temporary) home. FYI, Im from Australia.

So, the list of things (in no particular order) that are important to me are:

Climate: Id like a temperate climate that leans more toward the cold side. Probably not cold for a lot of people from the States, but something around 20-25 degrees Celsius (68 – 77 Fahrenheit) in the warmer months, and low enough for me to background snow (Im yet to see snow!) in winter would be perfect.
Sports: obviously college sports are a huge deal, and thats something Id love to be involved in while Im overseas, but Id also love the chance to go to a major sporting event while Im there. NFL is my sport of choice (go Bears), but failing that, NHL would be a great background as well.
National park/natural landscapes: Id love to be able to get away with relative ease to a national park, or something similar, to do hiking, simple mountain climbing (i.e. not much more than walking to get to the top, but great views!), camping, and just experiencing the beautiful natural wonders of the USA.
Education: Im studying physics, so a university that can help maintain a high standard of education in this field would definitely sway my decision
Tourist factor: Im hoping to avoid major tourists spots. I want to be a temporary citizen while Im overseas, not just a tourist. I want to background (however brief) a taste of real life as a university student/American citizen.

If anyone has any more questions that might help narrow down the choices, Id be happy to answer! If its any assistance, I took a random online quiz regarding places to live in the US, and it gave me a 100% match to Oregon based on my choices. Next closest was Washington with 87%.

The universities I can select from are:

American University
Arizona State University
Boston College
California State University
Georgia Institute of Technology
Kansas State University
Northeastern University
The Ohio State University
Purdue University
Rutgers, The State University of New Jersey
State University of New York at Stony Brook
Texas A&M University
The University of North Carolina – Chapel Hill
Tulane University
University of Arizona
University of California
University of Connecticut
University of Florida
University of Illinois
University of Maryland
University of Massachusetts
University of Michigan
University of Pennsylvania
University of Richmond
University of South Carolina
University of Texas at Austin
University of Virginia
University of Washington
University of Wisconsin – Madison
University of Wisconsin – Madison (ENG)
University of Wyoming
Washington University

Thanks in advance for any help/advice you can offer. I cant wait to visit your amazing country!