I found Split to be rather ugly compared to other parts of Croatia, but much of that has to do with it being a larger metropolitan city. However, the old part of town with the Diocletian Palace is very interesting. You’ll be in that area anyway, since the ferry service is right there, as well as the bus station. It’s very lively at night. I would suggest that maybe one night and one day would be enough for Split, although you might add another half day and see the ruins at Solin (which I’ve never seen but want to one day).
If you go to Hvar, know if you want to go to the town of Hvar or Stari Grad. The auto ferry stops in Stari Grad, but the hydrofoil goes to Hvar. You’ll save the bus or taxi ride from Stari Grad to Hvar if you take the hydrofoil. I’d suggest spending a night or two in Hvar.
From Split you might also want to visit Trogir (an easy bus ride from Split). Another suggestion would be to rent a car for a day and drive to Krka national park. The waterfalls there are very nice, and it’s a nice place for a cool swim in the summertime. Of course, the same can be said for the sea (though wear aquasocks and keep an eye out for urchins).
I don’t dive, so I can’t help you there, other than to say there were a couple of dive companies in Hvar.