Summer — June through August — is the obvious choice. Days are long, the weather is as reliable as it ever gets on the Atlantic coast, and ferry services to the islands run more frequently. July in particular sees some genuine warmth, though rain is always possible. The landscape is green and the coastal light in the evening is remarkable.
Winter brings short days, storms rolling in from the North Sea, and occasional aurora borealis on clear nights. The town is quiet and some services shut down, but if you are not bothered by cold and darkness, there is a particular beauty to the coast in this season. Spring and autumn are transitional — fewer crowds, unpredictable weather, and the same scenery at lower prices.