I can’t speak for your country - so I don’t know how much the names impact, including Purdue - but since you’ve eliminated.
My guess would be Michigan is the highest reputed around the world - known frankly for its football team than anything academic. Go Blue is known world wide.
I would step back - you have two remaining schools in cold areas - and UCSD. Funny, my son was in San Diego last night for a concert (where I grew up) and he sent me pictures - and he told me, this is the most beautiful city he’s ever seen!!
I was like yep - it’s known as America’s finest city for a reason.
Now I haven’t walked the UCSD campus forever, but it’s North of the city, East of La Jolla in what we called growing up the UTC area. Lots around - but the campus, if I recall, lots of trees, nature.
UIUC and Michigan are more traditional - and UIUC is polarizing. Some love. Some think it’s miserable. Both will be cold but UM colder in Winter as UIUC is a bit South.
UM is in Ann Arbor, generally considered a much better city than Urban Champaign. And if you’re flying in, it’s an easy hop from Detroit’s Airport - which has international flights. UIUC also has a small airport nearby but many would fly to Chicago.
UIUC and Michigan will have more sports, school spirit than UCSD, etc. Purdue too (Boiler Up) although you’ve eliminated it - but I do worry about why you did - as it sounds like you’ve not been to any - and are making a decision based on rank, etc. - your choice of course - but Purdue is known as an academic and fantastic institution - I’d think world wide. And it’s a much nicer (just my opinion - no doubt others share a different one) campus environment than UIUC, a more pleasant place to spend four years.
There’s more at play here in my mind - because the student has to spend four years, day after day after day.
But if you’re looking simply at rank, reputation internationally and I don’t know your country at all - but if someone made that statement to me and gave me the four schools, I’d say UM. It matters for where you live because it’s likely that’s where the student will end up in the long term.
Good luck.