I’ve never spent much time in either Appleton (Lawrence U) or Beloit, but both are fairly small towns. I don’t think there are any “must-see” attractions, but fall colors should be pretty good at that time of year (peak varies by year and by location). You might consider a short fall color driving tour if you have the time. Here are some possibilities:
https://www.travelwisconsin.com/article/things-to-do/11-scenic-drives-during-fall
Of those listed, the Door County tour and the Kettle Moraine tour are the closest to where you’ll be. Or you could do the Lake Geneva tour, as that’s more or less between Beloit and Lake Forest. October is also apple season in Wisconsin. I don’t have specific places, but if you get off the major highways you’ll probably run into farm stands, farmers markets, and u-pick apple orchards.
As for lodging, some of the usual chains are in both Appleton and Beloit but your choices may be limited. You could also look at nearby cities and towns. Appleton is just 30 miles south of Green Bay and 20 miles north of Oshkosh, easy striking distance. Beloit is 15 miles south of Janesville and 15 miles north of Rockford, IL, Same goes for dining options. I don’t think you’ll find much high end dining, so I’d go for local color, which will be more on the rustic side. Wisconsinites are very proud of their cheese, some of which is quite good, and all things cheese related, some of which is perhaps not so healthy, but kind of fun. Look for deep-fried cheese curds and beer-cheese soup. They also love their bratwurst. And the Friday night fish fry is a statewide institution. Wisconsin also has a strong German heritage and there are some decent German restaurants here and there, if that has any appeal.
Lake Forest is a high end North Shore suburb of Chicago. Probably limited lodging options in Lake Forest itself, but some nearby towns like Libertyville or Lincolnshire would give you more options.
As for University of Wisconsin campuses, there’s not really a public LAC like Minnesota-Morris. Apart from UW Madison and UW Milwaukee, the two research universities, most of the 4-year UW campuses are in the 8,000 to 12,000 student range. I hear good things about UW Eau Claire and UW LaCrosse, but they’re in the western part of the state, quite far from where you’ll be. There are also 4-year campuses at Oshkosh just south of Appleton, and at Whitewater, more or less between Appleton and Beloit. But I don’t know much about either of them.