Have you looked into the ABC islands (Aruba, Bonaire, Curacao)? I’ve only been to Aruba (and loved it – lots of good restaurants there, too). From what i understand Bonaire and Curacao are quieter. All three have an added benefit of being outside the hurricane belt and the trade winds help cool you off on a hot day.
Fripp Island SC. I’ve been there with my family roughly 10 times. It’s very relaxed, particularly near the south end of the island (but it’s not big anyway).
Rosemary Beach, gulf coast/panhandle in North west Florida. Beautiful area that will be very quiet in second half of August as all the schools in the south go back but all the restaurants/shops stay open because of labour day coming up. Spectacular beach (fine white sand 10 miles long and probably less than 100 people on it!) with beautiful water. Lots of good restaurants in the area. Easy 20 minute drive from Panama City airport. Really charming development in the style of an old Dutch town and with great facilities in terms of swimming pools, tennis courts etc etc.
We’ve been going for the last 10 years and would very strongly recommend it.
PM me if you’re interested and I can give you the low down.
August is Hurricane season in the Caribbean but it is early so you can get some great deals with not a lot of risk. It’s going to be hot but better than the gulf coast of Florida. If you want quiet beaches I would suggest St John, Soliman bay in Mexico or Virgin Gorda (harder to get to). Rent a house, kick back and enjoy.
If you are considering S/W Florida then by all means consider Sanibel Island. The perfect quiet beach vacation. Not a traffic light on the island. August is off peak so maybe you can get a decent price.
In terms of weather, NW Florida panhandle temps are almost never lower than a high of 80F and never higher than a daily high of 94F at that time of year. You could safely assume mid 80s to low 90s daily high and in the evenings high 70s. Fine for tennis in the morning, deep sea fishing (Destin is the deep sea fishing capital of the US!), cycling etc. You’ll probably get a couple of rainy days which will be cooler and are perfect for a shopping trip, movie, dolphin watching boat trip etc etc.
Re Sanibel, been there too. Absolutely zero in the way of dining options and everything other than lieing on the beach is a decent drive away. Beaches just as nice and quiet in Risemary. Naples is a different story and a great place all round but likely to be rainier than panhandle at that time of year.
East end Suffolk County, north and south fork, on Long Island has lots of quite beaches in August with as many wineries to visit. http://www.liwines.com/?cat=7