in summer Bay Beach but it sounds like this won't be summer (if game is included). For history sake though Bay Beach Amusement is a small scale on the water old fashioned style park with cheap rides (25 cents for toddlers, 50 cents for regular rides, $1 for the rollercoaster). The concessions are also cheap.
Bay Beach Wildlife Sanctuary across the street is open year round, FREE and worthwhile to check out.
Next the National Railroad Museum is a real treasure. They have events throughout the year as well to check out:
www.nationalrrmuseum.org/en-us/default.aspx (The Polar Express this year is sold out though).
Green Bay Botanical Gardens: http://www.gbbg.org/ This time of year they do the Garden of Lights.
The NEW Zoo:
Green Bay Children's Museum
We enjoyed our two night stay immensely at the Tundra Waterpark. If you have any questions on that let me know.
Edited: 10:49 am, November 19, 2012