Transportation in Split
If you are staying in Split and want to relax, we personally recommend going on foot. If you get thirsty, just find a cafe/bar, if you get hungry find a bakery or a supermarket (each has a deli counter with baked goods).
If you need to go to a beach further away, take an Uber or Bolt. The apps work like a charm, and you pay what is shown in the app. You will most likely be picked up by the regular city taxi, but at a reasonable rate. There are also numerous public buses, which you could try to brave using the Promet Split app.
Transfer to and from the airport is either by Croatia Airlines buses, which run at least once an hour off-season and once every 15 minutes in the high season (July-Aug) for the price of 8 Euros per person one way. They depart from the ferry terminal at the harbor and don't stop anywhere on the way. More comfortable is Uber/Taxi for 30 Euros in low season and 50 Euros in high season.
Transportation between the coast and the islands, e.g. Split to Hvar or Vis
We rely on:
Both options are cheap, safe, reliable and the way locals get around.
Transportation in Croatia in general
We typically take Bruno’s sister's car, connect our Spotify to the stereo and drive down the coast. We take the interstate for longer distances because it's in very good shape and tends to be relatively empty. Expect to pay around 7.50 Euros in tolls from Split to the bridge at Ploce that connects the mainland to the peninsula of Peljesac (and the southbound road to Dubrovnik).
But we have used local buses from Dubrovnik to Orebic on the peninsula of Peljesac a few times. It's inexpensive but of course less comfortable. Maria has travelled from Zadar to Split by bus a few times. To travel to the islands (Hvar, Vis, Korcula) we usually take either a car ferry or a passenger catamaran (for links to providers pls see above).
For day trips you may want to opt for a rental car/taxi/Bolt/Uber tour there and back, but we have never done that because it is more expensive and we would rather spend our money on an additional day's accommodation, restaurants and cafés and come back to Split a day later for the same total amount.