For a town of 2,500 people at 78 degrees north, Longyearbyen eats surprisingly well. The restaurant scene punches well above its weight — partly because there is serious money flowing through Arctic tourism and Arctic research, partly because Svalbard's tax-free status keeps some costs down, and partly because the chefs who choose to work here tend to be serious about what they do. Expect Arctic ingredients: reindeer, whale (still legal and eaten here), Svalbard ptarmigan, king crab, and various Arctic char preparations.
Huset is the institution. Kroa is the pub that does good food. Barentz Gastropub handles casual dining well. Prices everywhere are high — Svalbard is an expensive place to eat — but the quality usually justifies it.