My husband was born and raised as a British Expat in Hong Kong and loves the Chinese Cultural Center for its authenticity. There are some great, inexpensive and authentic restaurants there serving a wide variety of Chinese foods. There is a place called the Seafood Buffet on the west end of the plaza and the food there is fantastic and lunch during the week is around $7. Golden Buddha (next to the amazing wedding shop) has an inexpensive lunch menu and I've heard the Dim Sum is incredible. 

The grocery store in that plaza has tons of authentic Asian foods that you won't be able to find anywhere else. Just the smell of the different foods and spices takes me back to my last trip to Hong Kong and really adds to the experience. I don't know what half the stuff there is, but if you wander through the candy aisle you should pick up a few random pieces and just try something different. 

The Center has a festival around the Chinese New Year  where they have street vendors selling all kinds of goodies including a huge selection of decorative Koi fish and various cultural performances. It's really a unique place, especially here in Phoenix, and is worth an afternoon visit if you're looking for something different.