One week: that's just about the ideal length of time to discover the essentials of Corfu, some of its exceptional heritage, several of its magnificent beaches and nice seaside resorts, take a tour of the hinterland of an island full of relief, and even, why not, venture out for a day to the other Ionian islands!
However, you'll have to make some choices when you're there for a week: In Corfu, there are a thousand things to see, so if you have the chance, don't hesitate to extend your holiday to two weeks. This will give you the chance to explore the whole island, north, centre and south.
But for the moment, let's concentrate on the north of the island: hiring a car, even if only for the second part of the itinerary, is strongly recommended for complete independence of movement. As far as accommodation is concerned, don't hesitate to book as soon as possible: Corfu is a tourist island, and it's easy to fill up, so make sure you know where you're going before you leave!