It is really difficult to select one best onsen... especially if you know many of them.
Some are located next to the sea, and I great in summer. Others are in the mountains, and fantastic in winter after a day skiing. You might prefer large rotenburo ou smaller, old inside baths in historical buildings. Some onsen are great if you are with friends, and some are more pleasant if you are in couple or by yourself...
I am sure this answer is not helping you a lot!
You can have a look at Secret Onsen web site, at www.secret-japan.com/onsen where 120 onsen are rated, this would give you already a good idea of the nicest places.
If I was to choose one spot (rather than one specific onsen), that probably would be Kurokawa Onsen, in Kyushu...
But keep in mind that an onsen is a very personal thing, and your tastes might be very different that those of others.
I don't really have a favourite, I've only been to a few in my lifetime and I can't remember them by name, they were places I was brought to as a guest or that I stumbled onto by myself.
If you're ever in the Tokyo/Kanagawa/Yokohama area, then Hakone is just a stones throw away and has many incredible onsens within a relatively small area. Most are set into the hills and are all quite picturesque with varying levels of exclusivity. Hakone in general makes for a great 2 day overnighter. There are a few attractions there as well as lots of great hiking trails.
I'd have to say the coolest place I ever went to was a bath house in Kabe near Hiroshima. It's just off the main road which runs from Hiroshima to Kabe and beyond. It's in a large mall on the lefthand side in Kabe. It's not a true onsen, its a bath house, but it was (or seemed) brand spanking new, many different baths.. sitting ones, reclined ones, indoor, outdoor, wet & dry sauna, etc., the place was huge.
One of my favorites for nature, beauty, and the quality of the water was Kinugawa Onsen.
My favorite for simply enjoying luxury (and favorite overall, actually) has to be Akiho Onsen, at a place called Sakan. WOW, that was fancy! They even had rose petals floating in the baths!
I've also been to a lot that are pretty far out in the country, from Shikoku to Hokkaido, and they are wonderful in their own quaint way, but the lodging for some of them and the facilities tend to be kind of dirty and inconvenient. The nature, though, is really nice. Nothing beats soaking in a hot bath after a long day and breathing in fresh air and looking out at the mountains.
I am not a huge fan of onsens in general but I have been to some in Beppu and Yufuin that were quite nice. I was amazed at the sight of so many spiraling steam trails dotting the hillside when I first arrived near Oita.