Depending on how long you are spending in Asia, I wouldn't be overly concerned with the price of the flight. The longer you stay the easier you can make up that difference.
For example, in one choice you spend two weeks in Japan, the other two weeks in China.
The cost to fly to Tokyo is 800 while the cost to fly to Shanghai is let's say 1000. Over the 14 days you are there to make up 200 bucks, yo only need to save 15 bucks a day. Pretty easily done.
But for what's worth, I have priced out a few flights in the past from Florida to Asia and it seems like Tokyo (the only place I have flown into in Asia...my flight was 1000US) and Hong Kong (I think I saw a flight for 900 last year) tend to be a bit cheaper than Beijing, Shanghai and Singapore (I haven't looked much at SEA). Starting out in San Fran is probably going to make the flights a lot cheaper though...so good luck!
--Joey