May to early September is the practical visiting season. Daylight lasts almost the full 24 hours around midsummer — the so-called "simmer dim" — and the weather, although never reliably warm, is at its mildest. Wind is the constant. Even on a sunny day you will want layers and a waterproof.
June and early July are best for breeding seabirds — guillemots, razorbills, fulmars, and puffins are all in residence on the cliffs. The St Magnus International Festival, Orkney's main classical music festival, runs for a week in mid-June and is worth timing a visit around.
Winter is dark, wild, and quiet, but it has its admirers. The northern lights are sometimes visible from late autumn through early spring. Maeshowe's solstice alignment, when the setting sun on around 21 December illuminates the back of the chamber, is one of the most atmospheric experiences in Orkney.
Avoid landing in Stromness during a force-eight gale if you can — the ferry doesn't always run, and the crossing when it does is memorable.