Boerner Botanical Gardens
Check out their website for fun events and activities. These gardens are only 10 minutes or so from Greendale and they are surrounded by a massive nature park where you can go for long walks.
Boerner Botanical Gardens is an outside garden attraction. They have many different themed gardens throughout the park. It does cost $7 to enter, but it is well worth the time. There is also a wonderful gift shop in the main building and a small cafe.