You need a car, unless you are sailing. If it is winter you need to be prepared to drive on snow and ice. Snow tires and four-wheel drive would be helpful, as snowfall and drifting can get quite deep. Driving at night during a snow storm can be dangerous, especially because of the distance between towns with gas stations that stay open late. Be prepared to pull over and wait out storms; keeping a warm blanket in the back seat for this purpose is a very good idea. On the bright side, motels are cheap, if they haven't been abandoned.
There is very little public transit in the UP.
The pre-eminent scenic east-west route in the Upper Peninsula is US-2 along the northern shore of Lake Michigan. It follows the coastline very closely for miles and there are several areas in which you can pull off and park to access the beach directly, especially close to St. Ignace. M-28 also runs along the Lake Superior shore for long stretches, especially as you get close to Marquette, but contains the infamous "Seney Stretch", a segment of two-lane highway west of Seney, without a curve, bump in the road, or turn-off for 34 miles.
Large tracts of the Upper Peninsula are devoted to national forests, and are not breathtakingly scenic, although they do have their charm. An example of this would be M-28 through much of the central portion of the UP. However, for camping opportunities and the outdoors, M-28 leads to some extraordinary finds, as it passes through both Hiawatha National Forest and Ottawa National Forest. Another recommendation is going from M-28 to 94 through the Seney National Wildlife Refuge. Heading further north, US-41 takes you through the Keweenaw pronounced KEE we naw Peninsula, up to Fort Wilkins Historic State Park. This route takes you through beautiful forests, along the lakeshore via M-26 and offers sightings of many lighthouses and waterfalls. Sticking to the posted "circle tours" and following roads close to the lakes are probably your best bet for scenic road trips.
During the winter months snowmobiling across much of the UP is possible and trails are maintained.
Road and off-road mountain biking is getting more and more popular. Wear bright colors!