Bad time to travel? (weather concerns)

Hello! I was really hoping to explore Taiwan this coming weekend and the following week for my first time in Asia! However, I realize there was just a typhoon and I worry that the weather will not be ideal.

I am a solo-traveling, American, 22-yo man. I rock climb a lot and recently did a 9 day hiking trip up the American west coast, and was hoping to do some nature oriented activities in Taiwan.

My question is, will the weather make any hiking/biking or general exploring too unpleasant? And how about the nightlife? Do people generally stay in if the weather is too wet, or will the night markets / bars / etc. still be a good time?

Any advice is much appreciated. Thanks!