Rein,
You've gotten some great suggestions, Chicago Food Corp, 5-Continents, though specifically in Chinatown I have always liked the hardware store on Wentworth, which is now called Woks N Things.
We were in Chinatown on Sunday for a dim sum celebration of a nieces birthday, her and her sister always celebrate with dim sum, which I take a bit of pride in, since I introduced them to dim sum.
After lunch we wandered over to the Tea Leaf Cafe, one of the older nieces favorite spots in Chinatown, for bubble tea and I noticed a new hardware/cookware store. In fact, I bought a new wok spatula. I did not note the exact name and address, but it's located one door East of the Tea Leaf cafe. The Tea Leaf Cafe's address is slightly deceptive it's listed on Wentworth, but it's actually a few doors West of Wentworth on 23rd Place.
Speaking of Tea Leaf Cafe, it seems to be the 'happening' spot for the 18-25 year old Chinatown crowd,
As far as red bean buns, I agree with Pucca, St Ann in Chinatown Sq, Chiu Quon, with a preference to the Argyle St location and Richwell Mkt on 18th and Canal.
Enjoy,
Gary
Woks 'N' Things Inc
(312) 842-0701
2234 S Wentworth Ave
Chicago, IL 60616
Tea Leaf Cafe
(312) 808-3668
2336 S Wentworth Ave
Chicago, IL 60616
Actually on 23rd Place