The Hokke Club Kagoshima is a ten minute walk from Kagoshima-Chuo Station. It is very easy to find as it is on a big avenue, and you can take the tram if you want to - the hotel is practically on top of the tram stop. Inside, the lobby is very clean and nice (albeit small), and it is clean everywhere with no sign of cigarette smoke. I booked a single room which apparently has a semidouble bed. It does seem a bit wider than some single beds I've seen in Japan, but I wouldn't try to fit two people on it. The room is immaculately clean with everything you need. There is a hot bath, as is common in Japan, on the second floor, although I've not has a chance to use it. Wi-Fi is free and fast.
Overall, this hotel is great in absolute terms, and considering I paid something like 37 bucks for a night, the value is unbeatable as well.