For off mountain food, I agree with
@elogic about Genki burger. The burgers are delicious, generous and well priced. It was started by a couple of Aussie lads a number of years back, and is a firm favourite with both Aussie visitors and Japanese visitors too.
In the township itself, also try the Oyaki (a regional specialty). It's a soft steamed bun, filled with delicious sweet flavours (think red bean paste, sweetened spiced pumpkin, apple and cinnamon) or savoury flavours (pork, nozawana - a local green vegetable, I think it may be burdock, and other vegetable choices). The traditional place to buy these is on the main street corner outside Haus St Anton, where they sell thousands of these every day from a traditional steaming cart. Cost is 250-350 yen per bun. Don't worry if there is a long line, they serve fast, so be sure you know what you want before you get in line. In the past few years, a few alternative places selling oyaki have opened up along the main street, a bit cheaper and just as tasty, so have a good look around and give them a go - you won't be disappointed.
You can also get nice Aussie style coffee at Haus St Anton and now also several other places are also selling to the increasingly large number of Aussie guests. Spoiled for choice! Have a good look at bakery items too, as these are delicious! Haus St Anton, Akari Swiss Bakery and lots of others to choose from in the main street and little side streets just off it.
A short walk out of town, one of our favourite restaurants is the local izakaya Tonkitchi. It specialises in amazing okonomiyaki. You will need to make a reservatiotion to eat here. Your hotel can help.



