Pete is right. Just because she's Chinese doesn't mean there is some special set of rules governing what to do on the first date. It depends on her. Why not try asking her what she'd like to do? Novel concept, I know...
Some general rules for first dates-
1. Stick to dinner. Everyone likes to eat.
2.Make it some place nice, but not too expensive, since you should assume you are picking up the bill.
3.Ask questions that will give you RELEVANT information about the person and keep the conversation moving forward. Avoid dead end questions.
4.Don't get drunk unless she's getting drunk too.
5.Don't try and kiss her unless she comes on to you.
6.Don't bring up sex unless she does first.
7.Be yourself, even if you are a reprihensible person. She's going to find out sooner or later. Honesty counts for a lot.
8.Pay her compliments, but be sincere and don't overdo it .
9.Offer to pick up the bill, but don't insist on it.
10.Try and find some common groud. If you can't, then its probably a dud.