Downtown Champaign is a fine area. There are at least two dozen law students who live within a 5 minute walk of downtown. The main bus/train terminal is downtown, so bus access to the law school is not a problem. There are a lot of great restaurants and bars downtown. A couple coffee shops.
If you enjoy that smaller-city, local vibe, you'll get it here. There is a really nice park with free wifi, on the west side of downtown Champaign. Aptly named Westside Park. I prefer the nightlife downtown to that in the college area, and because it's within walking distance, I never have to worry about driving. Numerous law school events take place downtown, including Beer League Darts. The law students who enjoy a good night out tend to gravitate toward downtown, and this has worked in my favor. A few students, who tend to be just out of undergrad or who attended UIUC for undergrad, seem to stick to campus establishments for their nights out.
The streets and neighborhoods to the west and south west of downtown are charming. Scenic, with great character. A pleasant environment for a walk or jog. The Champaign public library downtown is a great alternative to the law school library.
Some law students live really close to campus, some in or near downtown, and many others scattered about in other areas more distant from the law school.