We stayed on one of the islands off Split, Brac - it was lovely and we caught the little ferry each time we wanted to go to the mainland (a few minutes' trip). Beaches, lots of history in Split and Trogir just nearby. Plenty of coach trips down the coast if you wanted to go further south for the day.
I think Dubrovnik nicer, but it's worth visiting both if you can. You could spend a day strolling round Dubrovnik, including going round on top of the city walls.
Check out the beaches here (not all that many are sandy; rock and pebbles are more common)
Hello, Personally, I would say Dubrovnik is probably the nicest part. There is a good beach in Uvala-Lapad Bay and the Boutique & Beach Hotel Villa Wolff is located just metres away from this. Details are here:
Bear in mind that many Ctoatian beaches are shingle not sand - or indeed non existent, so many resorts have built concrete platforms to sunbathe and swim from.
Also, the water tends to be a bit cooler than further south in the Med.
Like most places, the main resort beaches can be very busy with acres of east europeans or italians sunning themselves, but if you are prepared to go a bit further you can get away from people and of course, many of the beaches are CO.