The labyrinthine, bustling old town of Split is contained within the shell of the Emperor Diocletian’s magnificent palace, built in the late 3rd / early 4th century AD. It is quite spectacular; I stayed in a hotel right inside the walls. There are lots of different aspects to see – a Temple of Jupiter with a barrel-vaulted ceiling, the basement halls, the gates, as wells as other sights such as a huge Disney-like 20th century sculpture of the 10th century bishop Gregorius of Nin, a lovely archaeological museum with most of its greatest pieces outside in the courtyard (but also some nice things inside!) and lots of columns, arches and walls of the fabric of Diocletian’s great building all around the main area.
A short bus ride (the number 1 from Trg Gaje Bulata) from Split is the archaeological site of Salona, which boasts an impressive amphitheatre (a good walk from the entrance to the site) and a bath house, basilica, aqueduct, city gates and more. All in all, Split is a great place to visit with plenty to keep a Roman enthusiast busy!