I have visited Clifty Falls many of times while growing up. Last year, Ryan and I went on a hike there and we both can confirm that it is a beautiful park with lots of trails to explore.
Madison, in general, offers amazing shops downtown where you can find a variety of stores to choose from. Even if you aren't looking to shop while visiting, walking around downtown is also very enjoyable.
If you love to learn about history, Madison provides many museums and historic homes that you can visit. Some ones that I would suggest are: Schroeder Saddletree Factory Museum Dr. William Hutchings’ Office and Museum - Lanier Mansion Judge Jeremiah Sullivan House Shrewsbury-Windle Home