Salona, immediately north of Split, was Roman Dalmatia's most important city for five centuries — and Diocletian's hometown before he became emperor. The ruins are spread across a large site in the modern suburb of Solin: a 1st-century amphitheatre (partially standing), city walls with towers, early Christian basilicas, and a large necropolis. The site is substantially less visited than the palace in Split, which means you often have it largely to yourself.
The amphitheatre held 18,000 spectators — comparable to the one in Verona — and its outer wall survives to considerable height on the north and east sides. The early Christian material is particularly significant: a large 5th-century basilica complex, baptistery, and episcopal palace represent some of the earliest Christian architecture in the Adriatic world. The site museum (Tusculum) in the northeast corner explains the history clearly. Salona is a 20-minute bus ride north of Split and well worth combining with a day in the city.