Been to Sardinia 4 times, although the last visit was pre kids 9 years ago.
It's a beautiful place, the beaches are amazing, crystal clear turquoise blue, you can find many hidden spots off the beaten track and less crowded but you will definitely need a car to get to these. Also buy an umbrella, mats/chairs, cool box etc as there are no beach bed/umbrella sellers on these kinds of beaches. Main beaches are fine but you will be charged at least 40Euros a day for an umbrella and some chairs.
Food is great, towns are old but would say they are more traditional rather than ancient although some do date back. Your boys would love climbing and walking perhaps to these beaches too as some are a 10+min walk away after you have parked. Generally if you are driving on a main road and suddenly see lots of parked cars there then you should stop and have a look because that's where the locals are and the beach will be a gem.
Best thing about Sardinia are there are not really a lot of Brits (and before anyone says anything, I am one) but I love it because you avoid the usual drinking, loud, boring stereotypes you see on usual holidays.
I cannot sing this islands praises enough as you can probably tell!
I have stayed in both North/South, Santa Teresa Gallura (north) is a good small town you can get to from Alghero, small square with local nightlife every night (not clubs, restaurants mainly etc, children running around in the square, festivals if you go at the right time etc).
South has more variety in terms of beaches, more hotels etc. Villasimius in the South is lovely have a look, lots going on but not overly manic, cant really go wrong. Costa Rei also has stunning beaches, look at that resort.
I am waiting for your boys ages, best to do around this age if it's just you and family time you are looking for. It's not really a place to meet lots of other children/kids club type thing due to being more secluded, but obviously if you go to the main beaches they will be very crowded in August but a nice vibe. It's heavy on the Speedos as it is anywhere in Italy but to be honest I didn't' mind that as most of the people wearing them looked pretty good in them ha ha!.
Get a Lonely Planet/Rough Guide and take your pick. I cannot wait to get back to this island as it offers everything you mention and you do feel you are away from it.
The only thing you wont maybe is the temperature, it will be hotter than that in Jul and Aug as anywhere in the Med. Although in the North it always gets breezy at night whatever time of year you go so worth taking something to cover up with.
Sorry for long post.. got me thinking about this place again..