The MRT subways are really good. It goes pretty much everywhere (except the Costco...) and headway between trains is short. The stations are clean and (thankfully) air conditioned.
The easycard (悠遊卡) works on busses and trains and even most convenience stores. You can find cute card variations at a lot of 7-11s or at the Taipei Main Station.
For mainlanders, I learned that Taiwanese folks prefer the term 捷運 over 地鐵.
The trains themselves are the same as the ones on the shinkansen, so you know it's going to be good.
It's fast and gets you around the island. I got to take it only once, but it's really nice. Tickets are not super expensive and don't do some stupid demand/capacity pricing model.
It's the city bile rideshare. Great and pretty convenient. Biking infrastructure can be rough or nonexistant and it can be hard to plan routes.
Most recently (June 2021), YouBike 2.0, an incompatible upgrade, was rolling out. Kind of confusing.