What months have the best weather in the Fall or Spring, that is warm and driest for a 2 week trip to Beijing and Shanghai?

We want to stay at the JW Marriotts in the two cities and do some sightseeing, but mostly enjoy the local activities, food and people for a new cultural experience.

It seems this Fall is already tight for the hotels, but the airlines are more of a scheduling problem, especially the return, when attempting miles upgrades. CO and NW reservations make it feel like it is the first time they are looking for available dates, rate, etc. Even the Int desks are lost in finding connections with flexible dates.

Have enough miles with CO, AA, NW for Business or First class upgrades, but would prefer an Asian Partner airline. Perhaps Korean Air, or someting as fine as Cathay Pacific Air to recapture a couple of wonderful trips to BKK! I have not been interested in travel to China until this week.

Any suggestions would be greatly appreciated to avoid cold rainy smoggy weather, so that walking all around is possible!