South and East.
May is a great time to visit Iceland but bear in mind that many roads through the interior, Westfjords and along North coast can be closed due to snow.
Have you considered staying in farm accommodation (www.farmholidays.is
). They have superb accommodation throughout the island.
An example schedule for 7 days could be:
Day 1 - arrive Keflavik Int Airport and drive to Vik (numerous farmhouses around here)
Day 2 - spent day/night Vik, Dyrholaey area
Day 3 - drive to Skaftafell National Park area, overnight
Day 4 - drive to Jokulsarlon/Fjallsarlon area (stay overnight at Hali in Sudursveit - lovely farm)
Day 5 - drive to Stokkness peninsula/Hofn - return for overnight at Hali
Day 6 - return drive to Vik
Day 7 - return drive to Keflavik.
This would take in a range of landscape types etc and would give a good experience of what Iceland has to offer. Check out the schedules on my website: www.iceland-photography-tours.co.uk
to give you an idea of the locations covered