There are a lot of opportunities for biking in the Lansing area.
For the recreational cyclist there is the in 2014 expanded Lansing River Trail.
For mountain bikers, there is Burchfield Park and Anderson MTB Park, both within biking distance (less than 14miles from campus), so the perfect spots for those without car. Both parks are also listed on the trail guide of the Michigan Mountain Biking Association. Close to campus, but probably too far to bike there and back, are Fort Custer, Potowatomi Trail, Yankee Springs, Island Lake and Pontiac Lake. All of them are excellent trail parks that are only about an hour away by car.
For road cyclists, riding the DALMAC, one of the biggest cycling events in the state, is a pretty amazing opportunity. The DALMAC is a supported camping bicycle tour that kicks off here on MSU’s campus and ends 4 or 5 days later, depending on which route you choose, at Mackinaw City.
The DALMAC always happens during Labor day weekend, but sadly it usually coincides with the start of the semester, so you might have to skip a couple classes if you are interested in participating.
In case you are interested in doing your own tour the League of Michigan Bicyclists has route maps, some free for download, for all over Michigan.