Barrow has a handful of surprisingly decent restaurants given its extreme remoteness. Everything is flown or barged in, so expect prices north of ten dollars a plate for even basic meals. The town is damp -- no restaurant sells alcohol.
The options lean international: Korean food at Northern Lights Restaurant, Mexican at Pepe's North of the Border (touristy but fun), pizza with an Arctic Ocean view at Arctic Pizza, and solid Japanese at Osaka Restaurant. For a town of 5,000 people above the Arctic Circle, the variety is genuinely impressive.