Right on.
I think in August you should stay in the center since many places will be closed (imagine, it even just takes a few moments to find parking space!
), so if you went to a less lively area, it could be pretty dull.
Ummm....yes, in a way, the center might be quieter than usual at night on weekends, BUT less during the week since most people who do stay in town work a 'jornada intensiva', meaning only until 2:30-3PM, then go to the pool in the afternoon and go out most, if not EVERY night, to enjoy the much cooler night air (so do the tourists), and to make up for not being actually vacationing at the beach like most of their peers/family members!
I love spending at least part of August in Madrid!
The second week is great with the typical 'fiestas' of San Lorenzo and San Cayetano; on the 15th., there's the popular 'Virgen de La Paloma', Patron Saint of Madrid.