In 2014 we stayed two nights at this place: travel.lanyu.info/hostel/iratay-tribe/iratay
It’s on the southwest side of the island. The rooms are ordinary, nothing special. The owner (a fisherman, like most people on the island) picked us up from the harbor and organized a snorkeling outing (right by the airport; sounds bad but the underwater corals were great; and better than snorkeling near the nuke waste plant; we actually saw a group going there to snorkel) and a night flying fish catching boat trip (didn’t take part in that, cause felt miserable after throwing up my greasy fried rice with beef lunch; if you have a weak stomach, be prepared…). The place is also close to the airport and they rent out scooters. I kind of regretted not having stayed on the east coast for the sunrise. Had to get up before dawn and ride there, which is not too far (either cross the mountain or round the northern or southern tip; takes like an hour to ride around the whole island if I remember correctly; also remember, there is only one gas station, near the harbor, and the scooters strangely were low on fuel in no time. Ended up watching the sunrise from the weather station half way across the mountain (was spectacular). If you like flying fish for breakfast, they had a whole table full of it one morning.