JAL is good ka. I always fly to Chicago with JAL.
Korean Air is okay too. My friend just fly here using Korean Air.
IF you go with EVA, you have to stop at Taiwan, LA and come here ka.
I agree with others that it's quite late if you are looking for the ticket during this month for next month. But, Good luck to you ka. If you have any questions, drop me e-mail at email@example.com