Nasu-Shiobara (那須塩原) on the JR Tohoku Shinkansen line is the nearest station, about 1:15 from either of Tokyo or Sendai. A free bus shuttles passengers to some hot spring resorts from here; alternatively, it's 10 minutes on the JR Tohoku Main Line to Kuroiso (黒磯) station.
Because of its hilly terrain and the large area it covers, Nasu is probably best seen by car.
Nasu is highly volcanic and there are no less than seven hot springs in the Yumoto (湯本) area alone. The Nasu Onsen Ryokan Association  has a handy booking engine, but alas, only in Japanese.
Mount Nasu is a good spot for hiking and, in winter, skiing and snowboarding is available at Mount Jeans ski resort on the slopes of the mountain.
The Nasu Kogen (Nasu Highland) region is home to numerous "attractions", some more dubious than others, including a Monkey Park, Teddy Bear Museum, Car Museum and Animal Kingdom, where dogs can be rented by the hour (complete with authentic New Zealanders hosting a sheep shearing show).