After a quick visit to Zagreb in 2004 I made it back to Croatia as part of the Balkan tour in 2009, and I managed to take in Split and Dubrovnik.
Split has a very pleasant old centre based around the Diocletian's Palace overlooking the waterfront. The palace isn't one building, rather a series of old buildings surrounded by an old wall. I was lucky to get there very early in the morning before all the tour buses had arrived and had the place to myself. I paid my money and climbed The bell tower of Cathedral of St. Duje. The tower is very open so the climb up is quite scary, however the view of the city from the top was well worth the fear!
I wasn't quite so lucky with Dubrovnik, as the place seems to be very popular with tourists, most of whom seem to be shipped in from the huge cruise ships that moor off shore. There doesn't seem to be any time of day (or night) where there isn't some one with an umbrella being followed around by a herd of sheep.
The border of Croatia on the Adriatic coast is quite complex, and the road between Mostar in Bosnia and Herzegovina (BiH) and Dubrovnik in Croatia has three border crossings. It's not worth putting your passport away as it seems to be inspected every five minutes!