June through August is the prime season: the seabirds are nesting in enormous numbers on the western cliffs, the midnight sun keeps the sky bright past midnight, and the boat tours to the bird cliffs run daily. If seeing puffins and razorbills is the main draw — and it usually is — this window is non-negotiable.
May and September are quieter and still rewarding. The crowds are thin, the light is softer, and the island has more of its ordinary character. The bird colonies start to thin in September, but the hiking is excellent and the weather can surprise you.
Winter is a different proposition entirely. The ferries keep running, but the bird cliffs are empty, the mountain trails can be genuinely dangerous with ice and short daylight, and the island turns inward. The northern lights can be spectacular — Værøy's position well above the Arctic Circle puts it in prime viewing territory — but come prepared and come with realistic expectations about what's accessible.