I have been told that the most common accommodation style is billeting in people's homes
Croatia has the normal full range of accommodation hotels (of all standards, B&B/guest houses, apartments, hostels etc. I have found the following as a good booking site – www.booking.com
We did the following and it worked for us (we are a couple in our 60s but should be doable with a baby) –
Split 3 days (came in by hire car). The old town (Diocletian’s Palace) in Split is quite fantastic and shouldn’t be missed. You can easily spent a day looking around. I’d suggest starting with a walking tour -
http://www.splitwalkingtour.com/index.php/split-walking-tour.html
Ferry day trip to Hvar from Split
Ferry to Split to Korcula town (left Split late afternoon and arrived early evening with guest house owner meeting us at the harbour). The ferry terminal in Split is only a 10 minute walk from the Diocletian Palace and there are plenty of luggage storage options opposite the ferry terminal.
Korcula 2 days including a day trip (with a walk around the lake) to Mjlet Island (from Korcula).
Mini bus from Korcula to Dubrovnik (which includes a short ferry trip from Korcula to the mainland) Had a reasonable departure time (930am from memory) compared to the bus which was very early.
Used the following for the mini bus trip from Korcula to Dubrovnik, they will drop you at your hotel.
http://korkyra.info/about-us/
I’d also suggest a walking tour of Dubrovnik. It was free/tip based when we were there last October however I believe the Croatian authorities are cracking down on free walking tours (this was explained to us on our Split walking tour).
http://www.dubrovnik-walking-tours.com/?pid=37
The ferry and bus times vary depending on the month however I expect in June will have the full options but probably need to book at least a couple of days in advance.
Korcula town accommodation - Guest House Leon, small room but very good and great location (above the travel office mention above)
http://www.booking.com/hotel/hr/guest-house-leon.en-gb.html?sid=05589ccabe0e77cef1872ac0780c1b42;dcid=4;dist=0;srfid=7b3713d62a97a2a64d3e414fb6ddf9ebd301aa8cX1;type=total;ucfs=1&