There are many wineries in the Woodinville area. Chateau St. Michelle is the most famous and we also love DeLille Cellars. The more popular wineries will require advance reservations.
Rattlesnake Ledge is where Chris and I had our first date and is also very close to where Chris grew up. Its a relatively short hike (4 miles) with a lot of switchbacks but the view from the top makes it worth it.
Especially for guests staying in the Heathman, we recommend walking through downtown Kirkland and trying out the restaurants and bars. If its a nice day, the walk down the waterfront is lovely.