The situation in which there is no vacancy is rare but possible if you are attending during a large international business conference, but that problem is solved if you are willing to stay a few MRT stops away from the destination rather than walking distance from it.

You can often book using the internet, at the main sites like Travelocity etc, but these tend to be much more expensive than necessary. You WON’T save money by doing it this way, but you will save yourself the "OMG I don’t know where I am going to sleep!" feeling on arrival by doing it this way. However, if you fight that feeling you can save a few dollars and stay at a generally clean, affordable hotel.

A good rule of thumb is if it costs below 1200NT a night it probably is a bit sketchy or a hostel or something. At the 1200-1500NT range it may be very good or just a little weird, but tolerable weird. Above that you will probably get a quiet clean place. If you are paying over 4000NT a night you should be getting a very luxurious room with nice hot tubs and gardens inside or something.