The Mountain Bay State Trail is a good opportunity for a longer distance off-road run near Green Bay. It’s one of the longest rail trails in Wisconsin, running for 83 miles from Howard Memorial Park in the northwest part of Green Bay to Weston, just east of Wasau. The surface is crushed stone and is a fairly flat, easy surface. Much of the trail passes through open farmland. We’ve attached the full route map, and mapped the 35 miles between Howard and Shawano. There’s a brief road section there (well-marked), and the trail picks up again and is seamless to Weston. This information page has good descriptions of the specific sections.