This is a question there is no absolute definitive answer to. I have heard of suitable cool places: a spare bedroom (no heating on), garages, garden sheds and car boots, but it all depends on the weather. I was once storing and ripening a Camembert in my garage, and the weather turned warm when I was away and my mother was looking after the house. I got a call that said something like, 'I think there's something dead in your garage.'
Storing cheese in the fridge at too low a temperature means the flavour can be impaired, but if the weather is hot, sweaty cheese is hardly preferable.
The real answer to this question is to buy your cheese from a reliable supplier. You will then receive it in good condition so it's ready to eat, so the very best thing to do is eat it ASAP, otherwise store the cheese, wrapped carefully – with no cracks or bits showing – in either waxed paper or greaseproof or parchment paper, sealed with adhesive tape or an elastic band. If the weather is cool, any of the places mentioned above is suitable, if not then place it in the lowest part of the refrigerator. Clingfilm is not recommended, but I do keep my Parmesan in a polythene bag tied at the top in a cheese box in the fridge, and it keeps very well.