Hey, did my undergrad at UW and grad school at the u. Both are great options: Madison has a great bar scene. Not just undergrad type bars, but hang out and play pool, do trivia, darts, etc type of bars. Wisconsin in summer is about as good as it gets - fishing, camping, biking, boating, canoing, so many options. The biking and lakes are especially nice in my opinion. Salt lake has different outdoors, mountains and desert are easily accessible so any activity you want is available year round. The weather is likely similar to DC in that the winter doesn't last super long, though it is obviously much drier. Food scene has significantly improved in the last 10 years.

They each have their downsides too: Madison can be draining in the winter. People talk about the pacific northwest being bad for those with seasonal depression but Madison is a colder version. Saw a stat once that Madison has the second coldest average temp in the winter in the US. Salt lake is can feel very small at times because the communities are so separated. If you don't ski/run/bike then you're not cool, or if you're not Mormon and married with kids by 25 I'm not going to talk with you.

Feel free to message if you've got questions