St. Paul (MN) has a great science museum with a lot of good summer classes, and they often have classes during the year as well (honestly, as we only have used the summer programs, I don't pay as much attention to the ones during the year). I am not sure they have something weekly that you can just sign up for, but there are a lot of offerings.
I'm not sure about Chinese, but I am guessing in a metropolitan area this big there are programs (I know of a good Japanese program, but Chinese just isn't on my radar...).
We're in St. Paul - you can find about anything you want to do here. I know kids taking Chinese, French, German. My kids take Spanish. There are immersion schools for all of these within 15 minutes of our house. The science museum is amazing - my 10 year old is taking a genetics class there at the moment and took evolutionary biology earlier in the year. (Teacher has master's degree - great hands on) There are 2 smaller science museum that offers great classes/camps too (The Works, The Bakken). Leonardo's basement is great, there are children's orchestra concerts, theaters galore that all offer classes, the institute of art, Minneapolis College of Art and Design, U of MN GT Math programming, Edina Center for Excellece (offering math enrichment on the weekends). MacPhail center for music is excellent. Minnesota History Center has a fantastic network of museums, historical sites that offer kids programming. My kids take circus arts classes and my daughter takes dance. I've found the programming locally to be high quality. There is really too much available - I find it even hard to pick and choose. There is also a very active GT parenting community (MCGT - MN council for gifted talented).
Edited - thought of one more local resource for classes/enrichment. Minnesota Institute for Talented Youth has Saturday programming for 1st grade and up and summer camps. There are also a number of gifted magnet schools throughout the cities.
