I’m planning to be a biomedical engineer as a pre-med student. Obviously, UIUC is better known for engineering, but (correct me if I’m wrong) I think Madison is better for pre-med.
Academics aside, I’m also conflicted about the general environment of the school. Being a racial minority (Asian Indian, to be specific), I love the fact that Urbana is incredibly diverse, and I’m worried about feeling a little out of place at Madison. That being said, I’m in love with Madison’s campus and am not particularly enthusiastic about Urbana’s campus.
Thanks for any input!! 
Both are equally good for premed intentions (as are most colleges). Check each school’s website for the chances of getting the major you want. Biomedical engineering may be limited at UW with competitive entry due to facilities limitations in the numbers that can be handled.
You will need to decide whether you want to be a physician or an engineer. You also need to realize most with the intentions of going to medical school will not. This field is popular currently- a glut of neuro related majors in your generation.
Son is half Indian (H’s side) and went to UW. He is from WI and so was just like any other WI kid. There are now more Wisconsin born young adults- children of Indians who came decades ago. Madison has at least 3 different excellent Indian restaurants- one walking distance to campus, the others on the west side where there are also Indian grocery stores.
You can get an excellent education at either school. You decide which one most likely will let you get your proposed major. And which atmosphere you like best.
I think UW, and Madison in general, is much more diverse and international / cosmopolitan than Urbana. I don’t know where you got the idea that UIUC is so diverse or varied. True, both schools host a bunch of international students, but consider the overall feel of the area you will be settling in to study. UIUC is in a fairly bland part of the state of Illinois; Madison is known as the most culturally diverse and stimulating small city in the entire state of Wisconsin, and rates highly as a stimulating destination of this type in the country as a whole. Consider also this is one good reason why there have been so many out of state applicants from Illinois to UW, that Illinois students now have some trouble being admitted to UW.
One final note on diversity: UW has long been a top school for East Asian studies, along with Michigan, The University of Chicago, UC-Berkeley, and a few others. UIUC does not rate as highly for their history / language programs. While it is clearly not your department, you should take into consideration that there will be students and groups on campus with strong international ties doing advanced work and enriching the experience.
Academics you have a better idea – slight edge to UIUC for most engineering disciplines (but not all; chemical and bio-related engineering are strong at Wisconsin); edge to UW for bio- and natural sciences.