We spent a pleasant full day looking/walking around the central area of Zagreb (self guide walking tour from LP, museum of broken relationships and museum of naïve art were some highlights). Beyond that would need to look further afield.
I’d try to stay overnight at the Plitvice Lakes to give you at least half a day to look around all the lakes – they are quite fantastic). Not sure of the logistics of doing it by bus (we had hire car) – post 1 above should be helpful.
We considered a sailing trip option but unless you want to lie around on the boat to relax and swim it seemed a bit boring to us.
For the islands we did the following and worked for us –
Split 3 days (came from in by hire car)
Day ferry trip to Hvar from Split.
Ferry to Split to Korcula (left Split late afternoon and arrived early evening with guest house owner meeting us at the harbour).
Korcula 2 days including a day trip to Mljet 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
http://korkyra.info/about-us/
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.
Split accommodation - Apartments Posejdon & Neptun, was fantastic in the walls of the old city
http://www.booking.com/hotel/hr/osejdon-eptun.en-gb.html?sid=05589ccabe0e77cef1872ac0780c1b42;dcid=4;dist=0;srfid=3d032ea783826e0b0f8a52197950cad5395a4603X1;type=total;ucfs=1&
Korcula 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&
For Dubrovnik I’d suggest one day as a bare minimum, preferably two.
I’d recommend a walking tour to get you oriented –
www.dubrovnik-walking-tours.com
We did the Discover Dubrovnik walking tour and found it great. Tour guide was a local and very knowledgeable. Went for more than an hour and it was a free walking tour last year (the Croatian govt. is cracking down on free walking tours).
A couple of other highlights – walk around the city walls (do it early or late if there is a cruise ship(s) in town to avoid the crowds), the chair lift and museum at the top showing the history of the siege.