I've found the best way to meet local people in Taiwan is to smile and chat with them, everywhere you go. Most Taiwanese people have been studying English since grade school and can chat about most basic topics, with a large percentage of them being fully fluent in English from studying or working abroad.
Once you get passed the basic topics about why you're in Taiwan, what brought you here, and if you've every tried stinky tofu before, then you'll need to be more creative in keeping the conversation going. It's best to join a club or group of people who all do the same things, like on meetup.com.
Bars and clubs can be a fun way to meet Taiwanese who are uninhibited to speak English after a few drinks, although the bar culture is all about drinking with friends and not necessarily making new friends.
Taiwanese will always welcome foreigners but you will almost always need to take the first step and open your mouth. Give it a try and you'll be surprised at who you might meet and where that conversation will lead you.