Which month is better to travel to Prague? June or July?
There are school holidays from July for 2 months and most of native people are by sea what makes traffic faster. Crowds of tourists are there in June as well as in July, it does not matter. Summer could be quite hot and there is dry air, so it would be better to visit Prague in spring or autumn.
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It really depends, if you like heat then July will be hotter (too hot for me to enjoy the hilly hikes in the city). If you are looking for sunny mild temperatures (think light cardigan in evenings), then June is best.
To be honest, the difference is slight in terms of temperature. Yet consider that July is vacation season in Europe and Prague gets very busy. If not for the weather alone, you will definitely find the city friendlier, emptier (of tourists) and cheaper in June.
Enjoy Prague, it is a stunning city even in January! ;)
If you can swing May that'd be the ideal month. Weather is nice and although it is still crowded it is not nearly as crowded as July or June. However, if you only have those two months I would go early June since you might still get some decent weather and Prague is a city best explore on foot.