Corfu is VERY easy to rent cars right outside of port. If you drive you definitely want to see Paleokastitsa but, it doesn't take that long to get there via drive unless you want to hang out at the beach all day. Street signs unlike other Greek areas are VERY easy to follow. Near the monestary. If you are going to a beach go to the West side of the island. Best beach is Agis Gordis is a GREAT beach particularly for the younger. That is where the pink palace. St. Georges beach is also a beautiful area and has parasailing. Southwest side of the island. Downtown Corfu is also a short walk or taxi from the port and has alot of history as well as some fun cafes and shops. Hope this helps. Mouse Island was a disappointment in case someone pushes that.
Can't help with the other islands. sorry.