Lots of great options-
hiking- Sleeping Bear Dunes National Park- do the Pyramid Point Hike and Empire Bluff Hike. Both have amazing views. Also MUST do the Pierce Stocking Scenic Drive (if still open, closes for winter when it snows) In town near TC there are some great hiking trails behind building 20 of the Traverse City Village at Grand Traverse Commons (former state mental institution- must walk thru this building too!)
biking- bike east along the TART trail and it will take you down to the boardman lake, then bike back into town along 6th street to see the beautiful historic homes.
breweries- Right Brain Brewery, 7 Monks is not a brewery, but a taproom downtown with a great selection of MI beers. And a great atmosphere.
wineries- tons to choose from, but our favorites:
leelanau peninsula- black star farms, willow vineyards shady lane, mawby (for sparkling/champagne), verterra, tandem ciders (hard cider)
old mission peninsula- they are all great, but we like 2 lads winery, peninsula cellars, chateau grand traverse, chateau chantal
close to town- Left Foot Charley (in the Village at Grand Traverse Commons)