It seems that almost every family runs a Bed & Breakfast. Find one high on the hill with a good view of the lake and valley. The sight of the lake at dawn is not to be forgotten.Also try Obertraun, directly opposite Hallstatt on the lake, it is easily reached by ferry or train. The village offers good quality accommodation at cheaper rates, try the Obertrauner Hof in the centre with good access to shop, bank, tourist office etc.
Many are listed at (http://www.hallstatt.net/). Prices start at 20⬠with breakfast. Automatic online booking is rare.