I've already included most of my thoughts on this matter in the following thread:
http://www.flyertalk.com/forum/china...-shanghai.html
But, I will adapt this advice based on the proposed length of your stay. I guess I feel that 6 days is too long, and I'm not a fan of day trips because transportation is annoying and most places you'd consider going have airports of their own. Why not consider 4 days in SH and 2 days in Nanjing or Hangzhou (choose the order based on your overall logistics). If you're really feeling adventurous, Putuoshan wouldn't be a bad option: you can fly to/from there and take a ship between there and Shanghai. I only went there once, and that was 18 years ago (I understand it's considerably more developed now), but it was great for hiking and taking pictures. 1.5 days would be enough because it's a pretty small island.