San Francisco to Tokyo $457, to Singapore $580, Round-Trip (via Shanghai). LAX Also.

No visa is required for the overnight Shanghai stopover. February to mid-March, 2016.

http://www.airfarewatchdog.com/cheap-flights/San-Francisco-California-SFO-to-Tokyo-Tokyo-Prefecture-NRT/

http://www.airfarewatchdog.com/cheap-flights/San-Francisco-California-SFO-to-Singapore-Singapore-SIN/

http://www.airfarewatchdog.com/cheap-flights/Los-Angeles-California-LAX-to-Singapore-Singapore-SIN/

On China Eastern Airlines to Japan, on Air China to Singapore, both are reputable Asian carriers.

The Singapore route requires minimum 3-day stay.