If you can tear yourself away from the beautiful medieval city of Dubrovnik, Croatia's Dalmation Coast has myriad islands and a warm Mediterranean climate, and other cities nearly as beautiful (and definitely less over-run with tourists) than Dubrovnik.
The Elaphiti Islands nearby run in a chain parallel to the mainland, complete with inlets, caves and harbours, as well as seaside restaurants serving delicious fresh seafood. Further north lie several larger islands including the particularly attractive Korcula and Hvar, the new hotspot of the Dalmatian islands.
Hvar is developing something of a reputation as a glitzy rival to St Tropez and Sardinia, confirmed by the arrival of Russian oligarchs by the mega-yacht load. However, despite the glam and the glitz, the old town retains its original charm. The Old Town of Hvar is a hybrid of stone alleys and terracotta-roofed houses winding up the hill. There is a picturesque harbour with cobbled stones, a Renaissance cathedral, and a 17th century piazza housing the majestic St Stephen's tower, all serving as reminders of Hvar's history and heritage.
100 or so miles north of Dubrovnik is Split, the cultural capital of the Dalmatia region. The impressive 1,700 year old palace Roman Emperor (and Dalmatian resident) Diocletian built are now a UNESCO World Heritage Site surrounded by cafes, shops, museums and other cultural attractions. There are also plenty of good beaches, both in the city and the surrounding area.