If you want good Chinese food, you're really going to have to hit up Chinatown

China Pearl (9 Tyler St) is a favorite of mine for Sunday dimsum, but definitely not for lunch or dinner... If you looking for a good date place, you should check out Shabu Zen on 16 Tyler Street (
www.shabuzen.com). It's a Japanese Shabu-Shabu place, where you cook the food yourself in your own personal pot of boiling broth. It's a nice change from the usual Chinatown joint, and my bf and I have always had a good time here.
Sadly, the Copley area doesn't have too many good Asian restaurants, but I do like Chilli Duck (829 Boylston St) if you're into Thai. It's right in front of the Prudential Mall, so this would be prime location for you! Right next to it is Gyuhama, which serves up some decent sushi and other Japanese dishes. Also, there's a Pho Pasteur nearby (119 Newbury St), and when you're paying $6 for a big bowl of beef noodle soup, you really can't go wrong with that!

Personally, I don't think Kaya on Boylston is particularly good, but that's just me.
Good luck with your restaurant search, and have fun with your, um, date

Just remember to check if the restaurant you want to go to is open on New Year's Eve!