My recommendations

I haven't been everywhere, but I've been to a lot of places in Beijing.  If you get the chance to come here, this is my recommendations:

For Toys:

#1 Bairong World Trade Center

#2 Toy City behind Pearl Market at Tiantan

#3 Haggler's Alley, I know there are lots of them all over the city, they don't appear on maps.  Ours is near Bawangfennan, not far from Shin Kong Place

Souveniors:

#1 Qianmen- biggest selection

#2 Bairong World Trade Center- best prices

#3 Pearl Market/Silk Market

Clothing:

#1 Bairong World Trade Center

#2 Qianmen

#3 Haggler's Alley

Day to Day/Household 

Supermarkets:  Tesco/CareFour/YH

Bairong World Trade Center

Haggler's Alley

Fakes:

Pearl Market

Silk Market

Bookstores:

#1 Wanfuxing Book Store

#2 Foreign Book Store on Wanfuxing

#3 Xidan Boodstore

Chinese Finger Painting:

#1 Forbidden City- back row of shops

#2 Silk Market-on the stairs

Combo of Sightseeing next to Shopping:

Tiantan to Pearl Market & Toy City

Qianmen to Forbidden City to Jingshan Park

Sightseeing:

#1 Beihai

#2 Great Wall

#3 Summer Palace

#4 Botanical Garden

#5 Forbidden City

#6 Grand View Garden

Something Different:

Panjiayuan Folk Culture Market (flea market)

Ancient Observatory

Happy Valley Amusement Park