Cavtat is beautiful, as is Dubrovnik ... but only for a weekend or so.
Croatia is just too beautiful to stay in the one place too long. Within an hour or two of Dubrovnik, you have Mostar, Pelesac Peninsula, Ston, Korcula, Orebic, Medjegore (if it floats your boat), Montenegro .... you can go on and on.
Hire out a car and travel around, you won't regret it.