Something has died and is decomposing in the vicinity of your Hydrangea - it certainly isn't the plant itself. Check around for the carcass of a dead rodent, rabbit or bird...

Sounds like your hydrangea needs some attention. Remember (as name implies) hydrangeas love their water. Never let the ground dry out around them. Your bush may also benefit from some fertilizer. You can pick some up at the local garden center or hardware store. A couple inches of compost over the root zone is also a good idea. It will improve the health & vigor of your shrub.

Wave the flies away then look to see if there's anything crawled in there and died. If not, inspect the stems, backs of leaves and woody parts - you may have a case of hydrangea scale, so you're looking for white, fluffy deposits or egg masses. Otherwise, some varieties of Hydrangea do indeed attract flies if they produce non sterile flowers, they're attracted by a particular scent in the nectar, but this isn't usually a problem with the mophead types.