Los Angeles to Taipei $483 RT or San Francisco to Taipei $463 RT (travel Mar-May and Aug-Dec)

There are some under $500 roundtrip airfares travelling to Taipei, Taiwan (TPE) from Los Angeles or San Francisco.
From SFO, it will be on China Southern with two stops in China.
Depart March 21, May 2, 4; Sept 5, 9, 12, 14; Dec 2
Retuns March 27; May 8, 10; Sept 11, 13, 15, 18, 20; Oct 4, 11, 13, 16, 18, 20, 23, 25, 27, 30; Nov 1, 3, 10, 17, 24; Dec 8.
Use above dates and book it on Priceline .
From LAX, it will be on JAL with 1 stop in Osaka Japan.
Departs April 18, 19, 27; May 1, 9, 16; Aug 28, 30; Sept 5, 11, 13, 18, 25, 26; Oct 2, 5, 16, 17, 23, 30, 31; Nov 1, 6, 8, 13-15, 20-23, 29.
Returns: wide availability with minimum 7 day stays.
Use dates above and book it on Orbitz . The LAX-TPE pricing is not coming up on Priceline.
For up-to-minute travel availability, in case this post is live for a while, use Google flight search.
Sample itineraries attached from both cities. LAX-TPE is available over Thanksgiving holiday!