The OP didn't say s/he had to go into Taipei city. Taoyuan and Zhongli are closer--though I'd just as soon stay in the airport. What might be really practical for a couple hours, if the weather were decent, is getting a taxi and going to look at the fishing villages on the coast just north of the airport. There's even a park just a few kilometers to the NE up routes 4 & 15, according to the map--I've never been. Guaranteed not to be terrific, but not the airport either.