Hi Lanex,
Kurokawa is nice, but it's very small. You can really walk the entire area where there are preserved and restored buildings in a matter of minutes, so I was glad it wasn't a centerpiece of my itinerary in the area and was just a day trip from Beppu.
I do recommend Beppu because, with the sheer number of onsen there (some say there are 150), you're likely to find one or more that really float your boat. My favorite is Hyotan Onsen because it has a huge room with numerous waterfalls you can sit under. The massage the hot spring waterfall gives is sublime. You can move around to let it hit you wherever it feels good. I could spend hours under those onsen waterfalls.
Yufuin is cute, but it's also best as a day trip from Beppu. There are a couple nice onsen worth visiting there, but nothing in Yufuin knocked my socks off.
In other words, your best bet might be two or three nights in Beppu and day trips from there to Kurokawa and Yufuin.
Having been to Yakushima numerous times in different seasons, I wouldn't recommend late November. The mountains do get cold in late Fall because their elevations aren't trivial. Not nearly as pleasant as when it's warm. Plus the snorkeling on Yakushima's coast is good in some places, but not when it's relatively cold like in November. If/when you go to Yakushima, I recommend Sen No Ie (http://sen-no-ie.sakura.ne.jp), Moss Ocean House (
https://www.moss6.com) and Chinryu An (www.chinryu.com) for lodging, the latter of which offers a nice social environment and lower prices.
http://yakumonkey.com is a great resource on Yakushima.
Given your interest in nature, onsen and arts/crafts, I'd suggest stopping by Izu and the Fuji Five Lakes areas and hooking up with Izu Hike (www.izuhike.com) and Fuji Bike Tour (www.fujibiketour.com) as well.