The student unions are great. Yes, alone or with groups organized around these themes. Nothing as beautiful as in the mountains, but there are lots of nice places. There are also many tourist attractions near Madison which can be good for a bit of kitsch. Easier than a big city.
Most people seem to do just fine.
I wouldn't say easy, but it's certainly possible. Most grad students live off campus. Most students live in apartments or houses off campus. Parking around the department is a nightmare. Buses are free.