We went and loved it, will go back in the month of September with just DH when children older!
Its very hot. But gorgeous.
We got the hang of the local buses quite easily and enjoyed trip to Cavtat, ate lunch by marina, in awe of the amazing mega-bucks boats. (Its between airport and Dubrovnik). We went by bus but then came back by boat which was great.
We went on day boat trip to Lopud Island, as they have a lovely beach there, but it's not lovely in August, it was heaving. Not our favourite day!
Kayaking is very in, there are several places you can do it from.
We hired a car and went to Montenegro, lovely drive and beautiful place, had lunch in town called Kotor, stunning.
Really enjoyed the Cable Car. Amazing views from top.
Our favourite day was when we hired a guide:
www.toursbylocals.com/TBL/WebObjects/ToursByLocals.woa/1/wo/2TJulZOZ5hZ2LbGs1SwtKM/0.15.3.3.2.3
He met us and took us around the walls before it got too hot, his english is great as he used to work in UK, he took us to little ice cream/coffee places off the beaten track, knew where to refill our bottles with water, showed my eldest son lots of the Game of Throne sites, and then he left us at a great place to have our lunch. My two would have been 17 and 13 so similar ages to yours.
We stayed just outside the city, and my husband found a great website that showed which cruise ships were due in each day, some days the place has about 3 ships which equates to 1000s of people, they have to put ropes and one way systems in place around the pavements, it starts to smell later in the day, it's not nice! So we planned our days around cruise ships! That would probably be husband's TOP TIP!
This was one of our favourite places to eat (near the top of the city) Lady PiPi!
www.tripadvisor.co.uk/Restaurant_Review-g295371-d1797401-Reviews-Lady_Pi_Pi-Dubrovnik_Dubrovnik_Neretva_County_Dalmatia.html
Also this one:
www.tripadvisor.co.uk/Restaurant_Review-g295371-d3343994-Reviews-Restaurant_Kopun-Dubrovnik_Dubrovnik_Neretva_County_Dalmatia.html
Loved it!