I have a 3 free nights with hyatt to burn during my upcoming trip to asia, but I'm not sure where to use the free nights. I'll be going to Shanghai for 2 nights, Hong Kong for 5 nights, Korea for 5 nights, and Taiwan for 5 nights.

Having never been to any of these locations I'd like to not waste time staying at a fine hotel but sacrifice valuable time I could use sightseeing. That seems to be especially the issue with the Shanghai Hyatt properties which are quite distant from the main city attractions.

Any ideas?