The historic center of Split is relatively small, and for the most part, confined within the walls of the former Diocletian Palace. It's also unbelievably tricky to find your way. On my first foray into the palace to find my hotel, I accidentally found myself on the other side of the city center without any effort. So I had to get in again and navigate the narrow streets until I suddenly stood at the doorstep of Hotel Slavija.
One of the most lovely places around town is the Narodni Trg (People's Square), the heart of the Venetian city. It holds a number of terraces for lunch (octopus salad!) or just a coffee. Great for people watching ánd it's where the iconic 15th-century astronomical clock can be found.
The Roman remains of Diocletian's era are cluttered around the Peristilium, just behind the Silver Gate. This is where all tour groups end up; the square is busy all day. There's also a black sphinx at this location, which was brought in by Diocletian himself from a campaign in Egypt. His (former) mausoleum stands next to it, now a cathedral. A strange octagonal building full of exuberant sculptures and works of art.
Split might not be the most beautiful city on earth, but it has lots of ambiance thanks to its original layout. And it's a perfect transportation hub for the rest of the region, by bus or by boat.