I would like to visit Shanghai, but will be traveling standby. Can I get a visa?

Hi, it is hard to say, according to requirements by Chinese embassy, air tickets and hotel reservation are required for Chinese visa application. If you fly standby, you may need to provide a certificate or confirmation letter as proof.
BTW, I am not sure how long you will stay in Shanghai, there is a good news that if you have flight ticket leave for another country via Shanghai, you can stay 72 hours in Shanghai without Chinese visa.