As an outdoor enthusiast living in the Lansing area (since I was born), I've come to a stark realization. If one travels two hours north, you'll find outdoor area such as Boyne Mountain, Gladwin State Forest Area, Manistee National Forest, and Huron National Forest. To the south we find Red River Gorge, KY a huge rock climbing destination, and Mamoth Caves, KY. In the Upper Peninsula we find that between Sault Ste. Marie State Forest Area, Hiawatha National Forest, and Ottawa National Forest most of the U.P. consists of public recreation lands. But what's near Lansing? Unfortunately, not alot.
As far as recreation areas go there are a few, the best being Waterloo and Pinckney State Recreation Areas. These are connected together by one lower Michigan's best backpacking trails: The Waterloo-Pinckeny Trail.
Almost in Lansing is Rose Lake State Wildlife Research Area. This is 4,140 acres of great land for outdoor enthusiasts who find themselves shored up in Lansing.
For those who are closer to Eaton Rapids, Charlotte, or Holt Michigan then perhaps William M. Burchfield Park is a better fit. This is an Ingham County Park and will charge you $2 per car per day on most days. If you'd rather not pay the entry fee then check this map and you'll find that Burchfield (sometimes known as Grandriver) Park is connected to Riverbend Access Site, and McNamara Landing both of which have free parking from sunrise to set. So unless your business is actually in Burchfield park, try parking at one of the access sites and walking, biking or canoeing in. Did I mention that when there's no snow on the ground, Burchfield has some of the best mountain biking trails in lower Michigan. Burchfield park has ski rentals and snow tube rentals during the winter, however the classic toboggan hills have been closed until further notice due to lack of funding. Burchfield park rents canoes and provides canoe trips and kayak trips during the summer months.
Fenner Nature Center in Lansing has a good amount of land available for outdoor recreation. There are a few miles of trails available in this private non-profit area. You will almost always stumble across a flock of turkey or a deer or two. They have an education center, great for the kids, and are definitely worth your time for a quick escape into the "wilderness" in the city.
Good luck finding the right place to enjoy the outdoors in Lansing, Michigan. There are other minor parks and wilderness areas, but I didn't find them worth mentioning. I'd suggest you head away from Lansing any time you can to find the wilderness. Good luck!