Split: the palace is the city, and the beaches are a bus ride

Diocletian's Palace isn't a museum with a gate; it's the old town, and wandering its cellars (small fee) and the peristyle is free. Climb Marjan hill for the view over the harbor. Bačvice is the city beach, but the quieter coves on the south side of Marjan and the beaches at Kaštela are a short bus ride away. Apartments ("sobe" signs) are cheaper than hotels and often better placed; book early for July and August, when prices double.