From Taoyuan Airport to Taipei

For an adult, it costs around 180NTD for a single trip. You need to take the airport express to Taipei Main Station and then take Bus 49 to Kangding Rd. Intersection, you will see the hotel. To the airport, you can take Bus 513 to Taipei Main Station and the change to the express to airport.
As for kids, if they are less than 6 years & 3.7 feet, they can enjoy a free ride; if they between 6 and 12 years & 3.7 – 4.9, they can enjoy a half-price ticket; if they are more than 12 years or over 4.9, they need to pay the full-price ticket.

If travel from airport to the hotel by taxi, roughly how much will be the cost?

Well, the fare can be around 1,000NTD.