Sit on the steps
The red cushions belong to the cafe and cost the price of a drink; the stone steps are free and just as good. In the evening there is usually klapa — Dalmatian close-harmony singing — in the Vestibule next door, and the acoustics under that broken dome are worth standing still for. The cafe opens at nine and closes at midnight, and the cushions are the ones with the best view of the sphinx, which is the one thing in the square that predates everything else by a margin.
The rest of the palace around the square is in the Diocletian's Palace guide.
The sphinx
One of the black granite sphinxes Diocletian shipped from Egypt still sits at the south end. It is about 3,500 years old, which makes it older than the palace by a wider margin than the palace is older than you. Diocletian brought at least two of them; the other lost its head in the middle ages and the fragments are in the archaeological museum. The one on the Peristyle is intact, polished by three thousand years of hands, and worth a look in the morning before the cruise groups arrive.
What the Peristyle was for
It was the formal entrance to the imperial apartments — the colonnaded courtyard where the emperor appeared to his subjects, and where the approach from the sea terminated. The columns are Egyptian granite, the arches are Roman, and the whole thing was roofed in timber on one side and open on the other. The cafe now sits where the imperial guard once stood, which is a trade most people would make.
The approach from the sea still runs up through Diocletian's cellars from the Bronze Gate.
When to go
Before ten in the morning, when the square is empty and the light is soft. After seven in the evening, when the cruise groups are at dinner and the klapa singers arrive. Between eleven and four in July, the Peristyle is a crowd and you will be photobombed by someone taking a selfie with the sphinx.
In summer the square becomes a stage for the Split Summer Festival.
For the evening that follows, see the palace wine bars.
Things to do in Split
Split in one day
Boat trips and tours from Split