Chuck,
These hints are from family

Trade your $ for Ren Min Bi at the hotel, the shops outside will not be as fair.

Site seeing:

Great Wall - 8th Big Spot (or Landmark), the most crowded but the widest part of the wall, and there's 2 or 3 other spots that are further away.

North Sea Imperial Park, a beautiful park within the city

Shopping
Famous intersection for shopping for trinkets: Liu Li District (or Factory).
Friendship Stores don't suck.

Beijing Duck
Chuen Gui Dai Beijing Duck, (sounds more like Chuen Gai Da) ask for the main restaurant

Enjoy and travel safe!