Split

You don't need tickets for Diocletian's Palace because the palace is in ruins and the city was built around the ruins. There is no main entrance, so to speak, where you purchase tickets. The only place you need tickets for is the basement. We hired a private tour guide, Maya Benzon, recommended by Rick Steves, for a tour of the palace and the old town. She was excellent! You understand so much more of the history of Split and the palace. A private guide gives you a much better understanding of what you are seeing because there are no audioguides or pamphlets.

We also hired a private guide for our day in Split. If you have the time he can also take you to Togir which is very close. His info is Pero Ugarkovic email is lignja@gmail.com. He was born in Split and when not tour guiding is a marine biologist. A few friends have used him also and loved his tour.

You need to pay only for visiting specific buildings and places, like the city museum, the basement of the palace, the Cathedral, and the bell tower. Otherwise, you are free to walk around.

And the entrance fees are not huge.

We had a tour booked with Maya B. and she cancelled at the last minute. The replacement she sent was sub-par. You might want to consider another recommendation. We paid a lot and it was a disappointment.

There is no admission for Diocletian's Palace. You can enter the site, however for some locations (Cathedral, Jupiter's Temple, and some parts of substructures) you would need to pay the admission. Here is a good article about the palace https://www.tourdesksplit.com/diocletians-palace-split-croatia/
Anyway, I would also suggest you to book some of the local walking tours that would give you a great experience of this wonderful city.