My best advice is to organise a private tour with locals to get an in-depth feel and understanding for this city. This way you basically have a one on one with the guide, and you are able to learn a lot more than the superficial history of the place.
We did have a fantastic guide Katija and the driver Igor who understood we wanted to know as much as possible in the limited time we had and wanted more than the standard tourist routes.
Our first destination was the Diocletian's Palace which is a Unesco World Heritage Site. We began the tour labyrinth of Subterranean tunnels of the palace that was built in the 4th Century for Emperor Diocletian. The Palace has quite an interesting history with so many changes through time with so many other countries claiming this port. Exploring the ruins that are mixed in with current buildings gives you a whole new perspective of how cities progress.
If you are into art, especially sculpture head towards the museum of the famous Croation artist Muzejlivana Mestrovica and view his sculptures. My favourite was the one entitled 'Pieta' which he did 2 years after the tragic suicide of his son.
If you want to try some authentic Croatian cuisine, there's a lovely seaside town called Omis that has a nice outdoor restaurant, next to a clear stream called Radmanove Mlinice, although a tad touristy it has good food and I'd recommend the mixed grilled plate, especially the Cevapcici!
And when you finish your delicious local cuisine, do as the locals, find a cool place and take a nap!
