Some chocolate or sweets from the US will be nice.
(Especially when the family you planned to visit have children or teenagers.)
Just like the comments ahead, wine would be a good choice as well.
During Chinese New Year we are used to greeting each other by saying:
1. "新年快樂 (Xīnnián kuàilè)"
=Happy New Year
2. "恭喜發財Gōngxǐ fācái"
=I wish you have lots of money XD
Welcome to Taiwan!
If you come to Taipei during Chinese New Year at that time, I suggest you go to 迪化街(Dihua Street) to enjoy the traditional atmosphere of the Chinese culture. There are lots of fun stuff to see and TASTE :)
Centrum vitamin? Just kidding. Taiwanese love to ask their American relatives to bring vitamins when they visit.
Hmm, I'm not sure about giving wine. Most Taiwanese I know don't drink wine. And it's not part of Taiwanese culture to bring wine when you visit someone like they do in the west.
Almost everything in the US can be found in Taiwan nowadays so I can't really think of anything special.
I agree with chocolate, especially some famous high-end brand like Godiva.