sorry for my late response~
And It's nice to meet you
I live and work in Taipei, and begin to ride bikes for entertainment about three years ago
My boyfriend assembled a mountain cycle for me, and recently, I just bought a road bike frame
Actually, I'm still a beginner... So I don't have much experience of traveling around Taiwan
But here are indeed many beautiful places for a biker to look round
such as Hualien, Taitung, and any countryside of any county
Hope you have fun and enjoy the life here~