Most flights departing the U.S. arrive the following day. We recommend flying out on Saturday and arriving on Sunday to give yourself time to acclimate before the festivities begin.
There is a train station under the airport that will take you to Taipei Main Station, the main train station in the city. From there, you can take a taxi or Uber to the Grand Hotel. You can also Uber directly from the airport to the hotel (about US$40, 45 minutes), or take the CitiAir Bus (about US$3 per person, 90 minutes).
Public transportation is very easy to use in Taipei. You can get an EasyCard from any train station, and the funds on it can be used throughout the city, including 7-Elevens and in taxis. Uber is also very prevalent and cheap, as are taxis.
Most flights leave early in the morning, so we recommend flying out on Sunday morning, arriving back in the U.S. Sunday evening.