Chris,
Diving in Northern Taiwan is not as good as it gets. Southern sites (Kenting, Luodao, Lanyu) are better, but if you are up here anyway (I see you are living in Taipei), regular NE Coast dives are more practical.
Don't get me wrong .... it's not all THAT bad. Just you won't get the incredible biodiversity, viz., spectacular reefs, or depth that you can easily find down south.
NE Coast you're looking at Keelung-Yilan area, specifically Beitou Jow, the Canyons, Longdongwan, sites outside of the Longdong marina, Aodi, Toucheng, etc. In the past there have been some more adventuresome divers around who explored new stuff on their own, but I do not recommend this given your experience level. Contact a club in the city (every shop organizes daytrips), or just pack up your gear (if you own it), and head on out to the Pioneer shop or Northeast at Longdongwan (season and weather permitting).
Temp. and conditions in the winter are troublesome. Few of us dive all year round, but if you want to brave it, a 5mm is the minimum exposure protection you will need. I dive 7mm core under 3mm full length at this time of year. The sea is choppy, too - making shore entries/exits very dangerous. Honestly, the dive scene in the north is sparse throughout the winter .... but there are some diehards up here who would be willing to buddy up with you if conditions are favorable.
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