Onsen town in Japan - Oita Prefecture, Beppu-shi
Although it may have seen better days, to me the onsen capital of Japan still has to be Oita. I lived there as a JET in the mid-90's, so I might be a little biased. But most Japanese people will still associate Oita with onsens.
Beppu was like the Las Vegas of Japan for years, and with the economic downturn, has seen some of the glitz and glitter rub off. But in a way, that is some of its charm now.
Oita Prefecture has Beppu and Yufuin. Yufuin has a reputation as a more upscale onsen resort town. It's located in the mountains, beautiful scenery, and a nice town to walk around.
Beppu is gaudier, at least in the city, but if you go up the hill a little bit, there are beautiful ryokan with outdoor baths, private baths, family style...if you're interested in onsen, you owe it to yourself to check out Oita!