If you choose to visit Yakushima it's best to stay at least two nights, so you can enjoy the beauty and atmosphere of its ancient forests without having to worry about the ferry. A good place to stay is Minshuku Umikawa as it's friendly, comfortable, and convenient for transportation around the island.
The location couldn't really be better. It's on the main road just a couple of minutes' walk from Miyanoura ferry terminal, even less to the bus stop for buses to the island's attractions such as the forest trails at Yakusugi-Land, Shiratani Unsuikyo, and Gajumaru Banyan Garden. There's a supermarket immediately across the road for hiking supplies (they don't sell food at the trails themselves), a couple of souvenir shops just down the road, and it's an easy walk to the center of Miyanoura, where you'll find a handful of places to eat and drink.
It's only a small place, and you're greeted at the door by a big colorful painting. There are lots of wooden fittings and furniture, and you take your shoes off at the door, making it feel more like home. There are just five rooms, so you can't help but bump into the other guests, which adds to the comfortable atmosphere.
Despite being on the main road, it's pretty quiet, because there just isn't that much traffic; my room was also at the back, with a view of the ferryport from the window. The rooms are Japanese style, basic but cosy, with tatami floors, an alcove and a few hangers for storage, and plenty of spare futon blankets in case of chilly nights.
Elsewhere there are separate bathrooms for men and women, a fridge and washing machine for guests to use, and a lounge/dining room where you can hang out with the other guests or eat any meals you choose to take there. I hardly saw the proprieter Kenji, but he could speak a little English, and was boundlessly friendly and helpful on the few occasions we did cross paths.
Rooms cost from just ¥4000 per person, with no meals included, and you can choose to have breakfast and/or dinner at an additional cost. For the convenience and comfort, this really does represent good value.