If you plan to stay in Iceland longer, here are some places we like. Keep in mind that endless days mean you can travel well into the night.
The Blue Lagoon is really close to the airport, so head there when you land, or before you fly out. It's the most tourist-filled Icelandic destination, but pretty darn cool. Rub the mud all over your business and have great skin for the rest of your trip.
Reykjavik – the tiny yet cosmopolitan hipster-filled capital. Awesome bars, great coffee, weird/good shopping, and a good jumping off point for your travels if you're daytripping. Check out the Grapevine – the english speaking indie newspaper - for what's going on in the city.
Vik – one of the 10 most beautiful beaches in the world, a cute/quiet town, and a wool factory.
Jokulsarlon – an glacial lagoon full of insane blue icebergs melting off an ancient glacier, and drifting out to the open ocean. You can do boat tours here, or just stare in shock and wonderment. Stop to look at the receding edge of the Vatnajokull glacier on your way there – there is an awesome national park here and some great hour long hikes that you can't miss.
The golden circle - The most "touristy" places in Iceland in a quick and easy day trip from Reykjavik – super cool shit.
Lake Myvatn area – SO neat. You can stay in tiny Reykjahlid for a day or two and explore the whole area – it's diverse and unearthy and a bit wacky. If you like Game of Thrones, visit Dettifoss (it's where they film the stuff beyond the Wall). Here is a link to a good roadtrip/loop of cool shit in the area. Also, Myvatn Nature Baths rule!
The Westfjords – Our wedding is in the north part of the Westfjords, so, hey, you're already there! If you have a few days, love driving, and aren't dismayed by slow, bad roads, this is the true heart of Iceland. You won't see many other tourists. Tiny roadside hotpots (here is a map and a guide to some of them!) Other highlights are the bird cliffs of Latrabjarg (LITERALLY A MILLION FRIENDLY PUFFINS!!! Mike's favorite spot!) Dynjandi (the most amazing waterfall), and Isafjordur – a fun wee town and a good central spot for tours of the area if you're into that. If you like camping, and have warm clothes with you, you can camp anywhere, and bathe in the hot springs.
Here is a slideshow of some favorite places and things in Iceland.