A number of day trips are an easy drive from Champaign-Urbana, but many day-trip destinations are notable for their eccentricity or are otherwise offbeat.
Monticello, 20 minutes west via I-72. Features Allerton Park, is a University facility containing a Georgian-style mansion, large formal gardens, and some lovely nature trails.
A variety of Amish tourism destinations surround the town of Arcola, a 30-minute drive south on I-57. This area represents one of the largest concentrations of Amish in the United States. The attractions can be surreal, and include an Amish theme park almost a contradiction in terms called Rockome Gardens where it is possible to pay to play tic-tac-toe with a chicken. Other destinations include local Amish businesses selling specialties like Shoo-Fly Pie, Apple Butter, quilts, and hand-made furniture. Note that Amish goods have a reputation for being extremely well-made, not for being bargains. More information and directions are available from the Illinois Amish Interpretive Center.
The town of Arcola itself is also home to the official Raggedy Ann & Andy Museum, as well as the world's only Hippie Memorial, a 62-foot monument erected by local eccentric Bob Moomaw worth driving by if the weather is good. Arcola also boasts the world's largest broom and brush museum. More information is available from the Arcola Chamber of Commerce.
Rantoul is 12 miles north on I-57 or US-45. On the south side of Rantoul is the site of the former Chanute Air Force Base. Now it is the site of the Chanute Air Museum. The museum contains traditional indoor exhibits as well as a broad collection of aviation equipment and aircraft from WWII era up to a F-15A jet.
St Louis is a few hours away by train or by car.
Memphis is a 7.5 hrs away by Megabus or ~7hrs away by car.