You could take a ferry direct to Stari Grad, but an overnight stay in Split is an enjoyable experience. The attractions and shops stay open until 8pm, so there is time to explore the city even if you get a morning flight to Split. You can then take the 8.30 ferry to Stari Grad the next morning.
Some choices are:
Peristil Hotel. A new and of 3 star standard, just inside the walls of Diocletian's Palace, next to the cathedral. It is only a few minutes walk from the Airport bus stop and from the ferry. Simply walk through the market to the right of the old town walls and enter through the gate on that side. It is immediately to the left.
Palace Vestibul. This is a new, elite boutique hotel in the old town centre.
Hotel Park. Overlooking Bacvice beach, for many year's this was Split's sole four star hotel, with all services. It is a short walk from the town centre.
Art Hotel This practical modern cube is an ideal overnight stay, close to the centre of town. The rooms are stylish, reliably comfortable and spacious and there is a restaurant and bar.
Hotel President. A very comfortable, urban hotel situated in the very centre of the town of Split,
Bellevue. A pleasant overnight stay in the town centre.
Another good place to stay or visit on the way home is Trogir, another town that is a World Heritage Site. It is very near to Split airport. There is a left luggage facility at the bus station.
