What is your residence? Is it Hong Kong or the USA? If you are a resident in the USA you MUST apply for a visa at the Chinese embassy/consulate in the USA.
As of about two months ago.
The laws and rules change all the time. I mean--quite frequently. But as of a few months ago US citizens who are resident in the USA must get their visa in the USA. I've seen quite a few backpacking US tourists in the Chinese visa section here in Hong Kong walk away basically in tears that they cannot get a visa because they are not resident in Hong Kong. US Citizens who are in Hong Kong and possess a Hong Kong ID card can apply here in Hong Kong. The cost is also different depending on your passport. Again, reciprocity vs. the US costs for Chinese citizens and petty politics often comes into play, but you will pay more.
You will likely not be able to get a multiple entry unless you have previous Chinese visas in your passport. You may get a dual entry visa allowing you to enter twice within a six month period.
If you are planning on just a quick shopping trip to Shenzhen while in Hong Kong, save the money you would have spent on a visa and buy it in Hong Kong. If you are planning for a longer trip into China as a tourist, get the visa sorted out before you leave.