As a Croatian, I would definitely recommend spending some time in Split, as well as in Dubrovnik. Summer might not be the best time to go there since there are too many people and you don't get the real atmosphere of these places... if that's what you're after.
And, if you have a chance, don't miss out on some of the island just in front of Split - like Brac, Hvar or Korcula. They don't offer exclusive hotels, but are definitely worth visiting.
As far as Dubrovnik is concerned, THE place to stay is Hilton Imperial Dubrovnik -
http://www1.hilton.com/en_US/hi/hote...ovnik/index.do.
Enjoy Croatia!