This is in response to the post by jwcampbell asking for info on Mazu Islands - couldn’t access his message, so starting a separate thread.
I stayed at the Chinbe Hostel (芹壁村 – www.chinbe.com.tw) on Beigan Island in Mazu a couple of years ago. At the time, it was NT$500 per person (regardless of occupancy) to stay in the centuries-old old stone buildings that have been converted to hostels. It was very pleasant and atmospheric. There is a bar overlooking a small cove with a coral island that you can swim out to if you are a reasonable swimmer. Beigan itself is hilly and has great scenery – rent a scooter and circle it to spot various beaches and trail heads for swiming and hiking (be careful not to wander into the guarded military installations though).
The night we stayed there was a tide of anchovies that the locals waded out and caught with nets. We had lots of delicious fresh anchovies both fried and stewed over the next couple of days, and also some other delicious seafood.
There was no nightlife on the island at the time, and the nicer restaurants were only open for a couple of hours during lunch and dinner time - so don’t show up late for dinner. But for a simple, tranquil getaway (for those who like to hike or just sit overlooking the ocean with a book and a cool drink) you can’t beat it. It was a very short flight from Songshan airport.