Last minute trip to Split/Hvar/Dubrovnik

Hello,

I am flying in to Split in early June for work and then wanted to spend some leisure time traveling. So far I only have my flight planned into Split and then I have 5-6 open days before I need to leave. Ideally I would like to travel from Split > Hvar > Dubrovnik but I was hoping to keep my options open and not have to book lodging in each place ahead of time.

So my question for you, dear reader, is it relatively simple to arrive in Split and then travel to these destinations without knowing where I'm staying ahead of time? Will most accommodations already be full in early June? If I only have 5-6 days what is a reasonable amount of places to see/where would you focus your time? Any help is appreciated.

Thanks!