Edinburgh

No European city has a spikier calendar than Edinburgh. For most of the year it is a compact capital of half a million people that you can walk end to end in an hour. Then in August the Fringe, the International Festival, the Book Festival and the Military Tattoo run simultaneously for three and a half weeks, the population effectively doubles, the Royal Mile becomes a continuous performance, and accommodation prices go up by a factor of three or four. If you want the festival, come in August. If you do not, avoid it absolutely.

The second spike is Hogmanay. The street party, the concert in Princes Street Gardens and the Loony Dook carry demand from Boxing Day into the first days of January, and Burns Night on 25 January gives the month a small second lift. Beyond those two events, the curve is a modest northern-European summer bulge: July is busy and reasonably warm, June and September are pleasant, and February is the emptiest month of the year.

The weather never really justifies the peak. July, the warmest month, averages a high of 20°C and eleven rain days; the wind off the Forth makes any month feel colder than the number suggests. That argues for choosing on crowd and price instead, which points at late May, September and February. September in particular is the smart pick: the festival scaffolding has come down, the light is low and excellent on the Old Town, and hotel rates have collapsed back to normal within a week.