You could consider this hotel in nearby Taoyuan

http://www.monarch-hotels.com.tw/english/index.htm

Many airlines put their crew in there. Easy to get a taxi/limo there and back. (15/20mins when I did it. Also less subject to traffic snarl-ups that sometimes happen arriving/departing central Taipei). I'd only go into Taipei if you really intend to do something when you get there - nightlife etc.

For anyone with a day time layover, there are free half-day tours of Taipei organised by the tourist authority.

To be a real nightbird, you could whip around Taipei and do without a hotel altogether, returning in time to use lounge facilities. You can buy access to the "More" lounge. http://www.moregroup.com.tw/ NT$1500 (VIP), NT$1100 (normal), 50% for kids. Can't remember what VIP gets you, but I'm pretty sure the "normal" ticket gets you showers. Open 06:00 to 23:30.