Long before Diocletian built his palace and established Split, there was Salona, home to some 60,000 people. While still to be fully excavated (partly because there are ancestral olive trees in some of the would-be dig sites, but also due to funding and politics), it’s absolutely fascinating. Burial grounds, a remarkably well-preserved amphitheater, an early Christian church, and more await you.
If you can, I’d recommend finding a tour (the one I took isn’t still going), because nothing is labeled, and it would be pretty easy to miss the context. It’s still a cool place to wander around, though, so I would go even if you can’t find a tour. There is a little museum on site (Tusculum), but it’s more about the work of the Croatian archaeologist who began working on Split in the late nineteenth century.
Salona is about 5 km from the center of Split in the suburb of Solin. If you don’t take a tour, it’s a fairly inexpensive Uber, or, you could take the 1 bus (every 30 minutes). Make sure to have water and sunscreen and wear sturdy shoes, as the ground is not at all even.