V.L.
I personally love Destin or really any of the beaches in that area. I've also been to Pensacola. But I NEVER travel in the summertime. I have always gone in April and there are no crowds, spring break is over and it's just lovely and peaceful. Also, I have stayed at the Army MWR site there, which was tucked away from the main bustle of Destin.
North Myrtle Beach is great too, but I preferred more in my pre-child days. :) There are some beautiful places there, once I can afford to fly that way, I probably will give it another try.
If you go between June-August, any beach town will be busy and crowded. Even if you travel during the week. If you could, I would personally advise going in August because there are no holidays, long weekends, etc and towards the middle and end of the month people are starting to head home to get ready for school. But if you could postpone that long, then you might find it less busy.