My college major was math, and so most of my professors and many of my fellow students were from China or other Asian countries.
Hmm, what can I tell you...
Chinese people hate the food they serve in most American Chinese restaurants. There are apparently a few which do it right though. They usually say 'Authentic Chinese Cuisene' or something like that.
One thing I always like to do is ask questions which I already know the answer to. Ask her about Taipei 101. It's the tallest building in the world(as of a couple years ago, maybe there is a taller one now), and it's in Taiwan. Also, it's pronounced Taibei, not Taipei. Make sure to ask about the counterweight in the building which they made to protect it against earthquakes.
They also had an election there last year. The friends I knew who were from Taiwan were very, very excited about this. I believe he is a less traditional president who wants to have more open comminication with mainland China. So ask her about that, and what she thinks of him. You can try relating it to the new president we have in our country.
You could also try asking about Chinese New Year--That was on Monday, I think. There are other Chinese holidays you might not have heard of. The Moon Festival, which is in fall is the only one I can remember right now, but there are two or three others.
I never tried to speak Chinese around any of the Chinese/Taiwanese people I met, so I can't tell you what kind of reponse you'd get from doing that.
I don't consider myself an 'Asiaphile', but I do love the personality that women from those countries have. It is really different from here in the United States.