Here is a good hotel but spendy. However, right behind this hotel is a subsidiary with a GREAT free breakfast and really nice facilities. Close to MRT (out front and 15 minutes from downtown Taipei Main Station. Closse to night market and other shopping). Plan on about 1400NT per night. tripadvisor.com/Hotel_Review … ounty.html
If you take a taxi or bus from the airport, direct them to Banciao, Fuzhong MRT station. You will see the hotel. Right behind it is a smaller “Forward Suites” My friends from the States stayed ther for a week on their last trip. The rooms were spacios and clean with great linens and services. They negotiated to 1400 NT per night. PM me if I can help further.
Adoga.com is the way to go. I found a friendly and inexpensive homestay with them, Kiri’s House I think it was called, central location, in Da-an district which is nice. Kiri speaks English too.