I want to buy designer clothes and shoes in Beijing. Then have them shipped back to the US. Where?

Oh, you are suggested to go to Shiji Tianle Wholesale Market. Lots of stores there sell many clothes and shoes. Most of them have good quality and cheap prices. It's located at No.28, South Outer Xizhimen Street, Xicheng District.
After buying them, you can find a China Post and deliver parcels back to your country.