going to Taiwan during first week of December

As I know, the local CityInn is a pretty nice budget hotel with many branches, so you can choose to stay in any one of them.

For attractions, the Taipei Zoo, National Palace Museum, Maokong Gondola, Taipei 101 and Ximenting area are suggested to visit. Beside, if time is enough, you can visit the Yangmingshan, Cingjing Farm are worth seeing.

Hope you can have a nice trip in that city.