Regarding Split, spend a couple days there if you like ancient history and culture. If you're not into those things, Split is still worth seeing, but don't spend more than a day. You could also spend a day on one of the islands with Korcula and Hvar being the most popular. I prefer traveling up the coast by ferry rather than by bus. The busses I've been on are not bad, but can be cramped at times.
My favorite location in southern Croatia is Dubrovnik. We based ourselves in Dubrovnik for several days as it was a good base to explore Montenegro and Bosnia on day trips as well as see Dubrovnik itself. Without a car, you might consider a guided day tour to Montenegro (Kotor, Perast, Budva) or Bosnia (Mostar). There are multiple companies that offer both large (regular bus) and small (minibus) day trips and will pick you up from your hotel. It's by far the easiest way to see some places that you otherwise couldn't without a car.