If its your first time, it would be the capital Taipei. They're famous for the night markets especialy Ximenting which is the most famous， and the 101 building, the tallest in Taiwan. Short day trips out of town which I like are Jiufen and Shifen both accesible by public transport. And if you have more time you can spend a few days at Hualien, the east coast whic is also very beautiful.