A couple suggestions for you:

The Strip is on the south side of campus on Washington Street, runs from University on the north side to 6th on the south. This is if you want a bar close to campus.

Campus in general is gorgeous. IMHO it's better looking than UNL's campus. (I have relatives in Lincoln.) I think you will enjoy exploring. OSU has their own color/s of brick they use, even - they're consistent about campus and I think it really adds to the ambiance of it on a whole. The gardens surrounding the Union, on campus, are pretty, with Alpha Pond and some dope af ducks to accompany it.

Downtown is basically Main St from 6th to 12th - make sure to pass down at least once, enjoy Stillwater's only, and likely last, roundabout, with a nifty decoration in the center.