It's been about 5 or 6 years ago now, but my DD and I stayed at the Four Points Sheraton in downtown Chicago, they had an American Girl package. We really enjoyed our stay there and it is within walking distance of American Girl store. I'm not sure about parking though, we took the bus to Chicago. Have fun in Chicago!!
Just saw that you have twins. The AG packages will only include one doll bed, and the extra bed is, IMHO, not worth the extra they will charge (I think it's in the $50 range). Probably worth calling to ask, but if it is that much, you might do better just getting a parking included package at a hotel (still love the Drake ), and saving the extra money for spending at AG, or taking the girls to tea.
OP here- is there a Disneystore on the Magnificent Mile?