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.
http://www.baybeachwildlife.com/
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:
http://www.newzoo.org/
http://www.gbchildrensmuseum.org/
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