I will be staying in Xin Beitou for a couple of weeks and wondering if there are any good restaurants in that area for western or good chinese food?
Spring, a hot-spring hotel at Xin Beitou, has an offer (available through the 7-Eleven ATM coupons) for a nice set lunch for two plus access to their hot spring (the swimsuit-required group pools, not the private rooms) for NT$888 + 10%. That’s a pretty good deal.
Just a little up the hill from Spring is the Taiwan Folk Arts Museum, which is well worth visiting and also has a small Japanese-style restaurant.
Ah, Spring City Resort. Nice outside hotspring area… Good hint with that offer, that is good value for this otherwise not exactly cheap hot spring. Might be something for the next days if it stays cold 
I suggest getting the Japanese style set meal, not the Chinese one. While the Chinese one was OK for me, I was much more enjoying the Japanese style menu on the occasions that I was there. I am mentioning this because I feel this is not much of a matter of personal taste, but to me it looks like they put much more effort into the Japanese menu.
If I understand correctly: Until May 31, if you get money from any 7-11 ATM, you get this voucher. You have to make a reservation at that phone number, any day (also weekend) is OK. And yes it’s only Lunch (not Dinner), food seems to be the Japanese style that I liked a lot. Before paying present the voucher, you can pay by credit card or cash.