When to come — and when to absolutely avoid
By season
Quietest: Mid-January to early March (excluding Burns Night week) and the second half of November. Scottish winter weather isn't glamorous, but the indoor attractions are wonderfully warm, Crown Square has dramatic short-day light, and you can stand alone in the Great Hall for minutes at a time. The Argyle Battery view across to the Firth of Forth is at its most cinematic in cold, clear winter mornings.
Busiest: The entire month of August (the Edinburgh Fringe and Royal Edinburgh Military Tattoo), school summer holidays July–early September, and the Christmas–Hogmanay week. Avoid August weekends entirely if you can — the Esplanade is closed off for Tattoo grandstands. Easter weekend and Burns Night week (around 25 January) are also peak Scottish weekends.
By day of the week
Tuesday, Wednesday and Thursday mornings are calmest. Saturdays are always busy with day-trippers from across central Scotland. Mondays are surprisingly quiet because many cruise-ship coach tours stick to set itineraries that skip Edinburgh on Mondays. Sunday — note the One O'Clock Gun does not fire on Sundays, which keeps numbers slightly lower.
By time of day
The first slot at 9:30 and slots after 15:30 are noticeably quieter than the 11:00–14:00 peak when coach tours arrive and everyone clusters for the One O'Clock Gun. Aim for the very first slot of the day in summer; aim for late afternoon in winter to catch sunset light over the Firth of Forth from the Argyle Battery.