Taiwan to Shanghai to Busan to US

I'm flying from the U.S. to Taiwan for a few days, then to Shanghai for 3 or 4 days, then to Busan Korea for a few days, then back to U.S. I may be arriving in Shanghai at the Pudong Airport, but then leaving from the Hongqiao airport (or vise versa). Do I need a visa? Is it ok to arrive and leave at different airports in Shanghai?