There is lots of good walking to be done in the Nasu Mountain area. The walk from Nasu Mountain to Kita Onsen is a half day walk that takes you through some nice mountains and alpine vegetation. If you do it in Spring then there are some Azalias (Tsutsuji) near Kita Onsen. On the down side its much easier to do this walk if you have two cars because the start and finish point are not so close together.
This is an intermediate walk. If you don't walk regularly, you might want to do a few easier walks to build up to it. Its also a bit exposed and the weather is unpredicatable so I'd take a waterproof and something warm.
Start out at the Nasu Mountain carpark (map location). We had two cars and dropped one of them at the Kita Onsen carpark (map location) first. Climb to the mountain hut and then turn right to traverse along the mountain range. (you can also climb Mt. Nasu or walk to Sandogoya or Numappara from here too).
Once past the mountains there is some nice alpine scrub with Mountain Sakura. Then its a longish downhill walk to Kita Onsen. The path does split for a while and we'd suggest taking the right hand split because our the Azalias that are out in Spring.
Don't miss the opportunity for an hot spring at Kita Onsen. It has a great old building, a number of pools and a nice lobby area filled with friendly walkers. The giant pool in the front of the onsen with the water slide might put you off a bit, but there are more private and tasteful pools at the back of the building. I also recommend staying at Kita. (getting better photos and blogging Kita is a the list of things to blog)
From there is a short walk up to the carpark. Its probably possible to walk back to the starting carpark, but it would be a hard days walk.