For both Yamadashi in April and Satobiki in May (see schedule page for details) most accommodation in the Suwa area sells out well in advance.
That said, we always recommend checking with Masuya Guesthouse in Shimosuwa first. Run by the friendly and intrepid Kyon-chan, Suwa’s sole guesthouse is just a short walk from the station. Kyon-chan and her band of talented friends restored this historic building several years ago, becoming leaders in Suwa’s revitalization. For location, atmosphere, and friendliness, this is the place to be.
If Masuya is unavailable, as far as the Suwa area goes, you could try for a place in Okaya. Pickings will be slim there, too, and likely expensive if you do find a room.
A better bet is looking further afield. Matsumoto, a vibrant small city and regional hub, is probably the best option. In Matsumoto we recommend Matsumoto Backpackers, centrally located and run by a friendly couple.
Failing that, elsewhere in Matsumoto, or Shiojiri could work. Further south in Nagano (Ina), or even Yamanashi Prefecture (Kobuchizawa, Kofu) is a bit far, but still in striking distance. Any of the smaller towns on the train lines in between could be options as well.
Camping could be an option if you’re driving, but many official campgrounds will be closed especially during Yamadashi in April. Still, in a pinch it’s worth considering.
Or you could always go the couchsurfing route, too.