You have two choices. Weather-wise in Taiwan island. The northern region, Taipei, Taoyuan and Keelung City often have misty, foggy and cold weather during winter season.
On the contrary, southern region, like Kaohsiung and Tainan have mild weather. Pretty much breezy and about 4 hours of sunshine between mid morning to 3 pm in the afternoon. Plus, not too cold and freezing at night.