If you follow the link, number 7 on the map, the Old Wenatchee Bridge, is right across the street from the Cedar Inn hotel. The Loop Trail circles 13 miles of the Columbia River, hits several parks, and is a neat way to see the valley. I walked it in high school, and must warn you that unless you are used to walking 13 miles in a day, maybe just pick one of the nicer parts around a park. I had shin splints for 2 months afterwards! My favorite parts are between Pybus Public Market and Walla Walla Point Park.
This is Wenatchee's replica of the Pike Place Market in Seattle. It is a really neat market with restaurants and shops open every day, along with fresh local produce.
This hike is one of my favorites, and it is right in town. It is very popular to hike for exercise, and is quite steep in some places, however the view at the top is incredible. You can see every corner of the Valley, the Wenatchee River confluence, and get pretty dirty doing it. Bring lots of water and have a great workout!