In reply to idiotproof (Buxton MC):
You can go any time, even in midwinter; the landscape's starkly dramatic under snow and you have a good chance of seeing aurora. But for ease of getting about and half-decent temperatures, June-September are best, though you don't go to Iceland for sunbathing, and there's a risk of remoter roads flooding at any time of year. And it doesn't really do 'pretty places', a lot of it is spectacularly stern verging on awesome, even if there aren't any current substantial eruptions - though in the nature of Iceland, there's almost certain to be another one coming alone quite soon, and there are various places where you can see the ground steaming and feel it warm under your feet.
Easyjet now flies from various British centres to Keflavik, the primary airport, about 45 minutes from Reykjavik. Reykjavik can hardly be escaped even if you'd want to, since it has a great chunk of the total population - most of Iceland is either empty or very sparsely populated - but it's also the centre of culture, entertainment, etc.
Car hire is expensive and it's a long way between places, often over barren lava plains, so four days won't take you far unless you really work at it. The Golden Triangle mentioned by ben b is the very popular tourist circuit in the SW that takes you to key sites: Blue Lagoon (organised thermal-pool swimming), Thingvellir (site of ancient parliament, dramatic geology), Geyser (geysers!) and Gullfoss (impressive monster waterfalls). Best to allow two days for that. Lots of bus/minibus tours available if you want to avoid the driving.