I'm staying here in a few weeks on a 20-ish hour layover. I looked into hotels nearer Tayoyuan but ultimately decided that the MRT is fairly efficient and didn't like the hotels near the airport anyways.
Last time I stayed here it took me about 1.5 hours to get to the hotel from the airport. Airport to airport station, waiting, and travel time to Taipei main station was 54 minutes, 10 minutes walking to other line, and another 20 minutes on that line to the Grand Hyatt. When I left the next day I took Uber to Taipei main station -- not sure that was worth it... only NT$205, but still took 20 minutes, but this was a Thursday morning at 8:30AM, so that might have had more to do with it. This time I'm leaving on a Sunday morning so may do the same thing again.
Just wanted to comment on my transportation and if anyone else has suggestions let me know!