I wish the subject line read "our week in Taipei," but we only had the 23 hour layover from Denpasar headed back to Chicago. I think there's a strong possibility we will return next year for several days in Taipei, the little we experienced was amazing.
If you find yourself connecting through Taipei overnight with EVA Airways as we did this week, please do yourself a favor and go see Taipei. Our flight arrived from Denpasar around 9:15PM on Monday. The departing flight to Chicago was 8PM on Tuesday, more than enough time to see a sliver of this beautiful city. My wife and I booked a standard room at Hotel Relax I, conveniently a five minute walk from Main Station and TPE MRT. Due to the arrival time, we found a taxi from the terminal and 35 minutes, $30 USD later we arrived. The following afternoon we used the TPE MRT back to TPE, I think it was $14 USD for two adults one-way. Highly recommend this service, easy to use and you'll see more of Taipei as you're departing.
With a handful of hours to sleep, the next morning we decided to see what I consider a marvel of engineering and incredibly beautiful, Taipei 101. I know there's probably 15 other things people would recommend, but with limited time and no knowledge of Taipei this was a great fit into our schedule. Using the Taipei metro system is very easy, English is not an issue to navigate the ticketing kiosks or metro itself. Taipei 101 was amazing, well worth the visit despite 80% cloud cover. Accessing the observatory is a bit of a labyrinth as you navigate through a mall and series of escalators and elevators. My wife and I spent about 90 minutes walking around the observation floor, having coffee and taking in the city between clouds. We had no idea what a damper was in a structure, but now have a fond appreciation for dampers and their babies :)
Following our visit to Taipei 101 we slowly returned to Hotel Relax I where they will hold your luggage after check-out. Fortunately our checked bags were held over by EVA Air, so our two backpacks and laptop bag were easily managed. The TPE MRT is fast, affordable and very comfortable as we you begin transiting back home. Our 23 hour layover was realistically 14 hours in the city, but well worth it. We hope to return next winter and explore more of this incredible city.