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So it's important to know what mood you want to set.
Based on that, what do you think would work better: A dinner at a fancy restaurant? A fancy restaurant (even for your typical Asian woman with regards to her culture) will implicitly tell her that you're a safe guy who wants to provide for her.
If that's what you want to convey then fine..let me tell you a personal story that you might relate to. Instead he took her someplace new that was fun.that he could be alone with her.
Online dating tips are available for men as well as women, for all stages of relationships.
If you're looking for something a bit more original than the typical "dinner and a movie," more power to you.