R.N.
I had my son's first birthday party at Gymboree Play and Music in Prairie Village. THey also have gyms in Olathe and Overland Park and celebrate up to 5 years. They have activities provided so the 'messy' thing would be out. It was a GREAT time and very little work for my family (no cleaning).
You could try the gym at your local elementary school. Technically, you pay taxes for it so it may be available for your use.
R.