You can find everything
The Taipei Night Markets (台北夜市) are worth a visit for the variety of products and people you can find. After a day of seeing the sights and a little rest at the hotel, you can head to the markets which pop up at dusk and stay open until well after midnight (they close around 2am).
In these markets you can find everything: clothes, food, paintings, toys, videogames, antiques, acupuncture, and massages. It reminded me of a flea market, but at night. There are different types of stands: those which are essentially stores which they drag out onto the sidewalk and those which occupy the spaces between (they're technically illegal, but the police seem to give them the blind eye).