I biked quite a bit while living in Beijing (10 years ago) and it was great. Best way to get around the city. I've spent some time in Shanghai but never biked. It's probably less bike friendly than Beijing, but any major city in China will have tons of bikes.

Two pieces of advice from my Beijing days:

1. Go with the flow. Most riders take a more leisurely pace.

2. Watch out. Drivers are nuts.