Great idea @Fighter.
Ohio State: Grew up there going to games in '70s and early '80s, so I'm biased. One of the great gameday experiences and stadiums, IMO. After I became a student at Illinois I had a nice 3-0 run of seeing the Illini beat OSU there in 1988/1990/2001. That 2001 game was the season after they lowered the field and virtually closed the horseshoe. Loud AF. We beat them anyway

. Sadly, haven't been to a game there in >20 years.
Iowa: Saw the Iowa-Michigan game there in October 2003. Fantastic gameday experience, blue skies, peak fall weather. Seems like everyone in the state of Iowa is tailgating there. Excellent BBQ pork, as I recall. Kinnick is a great place to see a game. The contest was really exciting, too. #22 Iowa prevailed over #9 Michigan 30-27. Probably the only matchup when I would ever root for Iowa, lol. Saw a fun women's volleyball game the evening before in Carver-Hawkeye. The Cubs were rockin' the NLDS v. the Braves at that time (it was 10 days before the Bartman meltdown) and we enjoyed watching the game that evening in a campus bar. A good time all 'round.
Michigan: Saw the 2001 Illini loss there (45-20). Such an ugly stadium: a giant featureless bowl. The best I can say for it is no obstructed sightlines. As I left the stadium a guy around 30 taunted me for my Illinois sweatshirt. I shot back that he'd better enjoy this short-lived feeling because at least I'd enjoy
two beat-downs over Michigan during the coming basketball season (they were the dregs of the conference at the time.) He kinda choked at my retort, laughed and sheepishly said "Touché." That felt good, at least, particularly because there was a crowd who heard it and they all saw an Illinois Man put a Michigan Man in his place swiftly and publicly. And indeed we beat them by 24 in Champaign and 8 in Ann Arbor, and they finished in 10th place.
Penn State: Saw the 2008 Saturday night, ESPN-prime time #22 Illini loss to #12 PSU 38-24. PSU won the conference that season. I really believed nothing in the BT could top seeing a game in Ohio Stadium. Penn State equaled it. Capacity crowd, night game, spent all afternoon in the campus bars watching football. Just a great experience. Stopped by Rec Hall and saw part of a volleyball game there. It was designed by the architect who designed the Palestra in Philly (IMO the finest college basketball venue in America). PSU basketball played there until that awful Bryce-Jordan Arena was built in the '90s. Anyway, it's a great arena, holds less than 7k and would be an entertaining place to watch a basketball game if they still played there. Huge home-court advantage (as if we don't have enough trouble beating them on the road as it is.)
Syracuse: Saw the 2007 Illini 41-20 victory there in the Carrier Dome (now named something else.) I'd seen games there with my brother (who has lived there for 40 years) back in the Donovan McNabb days in the '90s. When that stadium is full and Syracuse is good, it rocks. That year Syracuse was meh and the fans/students weren't too juiced, tho' we were

. Syracuse's campus and the campustown is lame. Such a depressing city, as I know all too well from a lifetime of visits to see family there. Also have been to several NCAA hoops regional finals in the Dome; great venue for that, too. And I'm no fan of basketball or football in domed stadiums.
Northwestern: 1987. Dyche Stadium, atmosphere, weather, Illini performance: *
gack*, across the board. 3-7-1 season. Mike White resigned two months later.
Purdue: ???? Heading there in 24 days for the game. Can't wait.
Maryland: ???? Will be there in mid-October for the game. My expectations of the venue are low. Even my ex-Maryland hoops player buddy admits it's uninspiring. They have a decent team so I hope the crowd is good.
Gotta hit Madison for an Illini game at some point, and also Michigan State.