picture the following. A tourist island that the last few years is not that popular for varius reasons... i believe you will be able to get something if you are interested only in sleeping. for the breakfast i cant be sure.
just in case make a small booking in a hotel in the area you are interested for a couple of days so you will have a place to sleep when you get there and the next day/s go out looking for something that u will like. in the case you are thinking of end of june it will be little bit more hard to find something but that is not said in order to make your hope go.
the truth is you will see lots and lots of rooms/apt signs to rent. so you will manage.

Hi - I always go flight only to Crete! This way you can choose your accommodation and how long you stay in one place - you'll have no problems finding somewhere.

What I generally do on arrival (if it's a night flight) is phone a hotel in Heraklion to check they've got a room for one night and get a taxi there before continuing on by bus the following day.