The country - specifically the south-west of the country - has pivoted to embrace their geography. Iceland is very pretty, and full of tourists like you. No matter what you do, you will enjoy yourself. Also, it is very small. You can definitely drive the whole thing pretty easily.
Iceland is rural.
There are many pleasant guest-houses, but towns are largely functional and oriented to supporting hikers rather than walking-tourists. Iceland's big thing to see isn't a church or a museum, it is waterfalls and cliffs and glaciers. In June and July, it is also puffins.
Iceland is an island.
Things cost money here. Things cost approximately double in Iceland what they do anywhere else. Groceries are the exception - they cost about the same amount as they do in downtown Toronto. Everyone not from a major urban centre is in for some sticker-shock.
There are a lot of people in technical clothes, make yourself liked by wearing human clothes.
North Americans are not the only visitors. Stopovers apply from Europe, too, so you will see fit Germans and rangy Italians and everyone in between. They will be wearing technical gear. You will become fluent in the language of what technical gear belongs to which country. If you see fancy-ass North Face, it's American, and they are from New York.
What this means is that Iceland is a tourist economy and they have a high season, and you are probably going in the high season, and they are fully prepared for you to come and be entertained with beautiful rocks, so tip at coffee shops and bars and act like the natural resource extraction you are. But be human about it.
Blackout curtains are a lie.
If you're there in summer and you like dark, at all, you are shit out of luck, because that isn't a thing Iceland has in summer. It does have the sensation of endless afternoon naps, though. I love afternoon naps. I've heard some people wear eye masks, but they fall off your face at night.
Special tourist things are expensive and fun.
I paid to go snorkelling in Silfra and to ride an Icelandic horse at Laknes Horse Farm. I would like to see a lava tunnel, though I have not yet. These things are expensive. They are also 100% worthwhile. Most things have The Blue Lagoon attached as part of a package deal. Book up your Blue Lagoon overnight dates, as those book early, but it's fine with daytrippers.
Book everything in advance.
This is almost wholly a tourist and sometimes farming, fish-processing or aluminum-manufacture economy. Things book up with other tourists. Book in advance.
If you find fish soup on the menu, order the fish soup, it is invariably excellent. There is a lot of fish soup. If fish soup is not to your taste, or you are allergic to shellfish which form the main broth for the soup, the other option is lamb, which is omnipresent and very good. If you are vegetarian, you're in for an expensive trip filled with self-cooked meals.
Hit the duty-free. Booze taxes in Iceland make Ontario and Pennsylvania feel like New Orleans or Montreal, in terms of price, and there is a 24% VAT on basically everything nice in the world. At Geysir you can buy a bottle - a bottle - of beer for $18.
Sheep come in groups of three.
Sheep are everywhere. They are behind your guest-house and on your plate. They hate people - as would you, if your interaction with people were death and forcible hair-cuts - and have a wicked turn of speed, so if you want a photo, be fast on the shutter. Do not resist the sheep. They are your destiny.
Reykjavik is tiny.
Reykjavik is tiny. Like, smaller than that tiny. Everything in Reykjavik is entirely walkable, and there are only perhaps six cabs in the city, total. Mostly, tours and transit to tours is provided by Reykjavik Excursions, who also run the Fly Bus from the (excellent) Keflavik airport for about $20 a ticket.
There is a very small shopping district, which is incredibly expensive, and has some okay gift-shops. You can get whatever you can find in the gift shops at the airport.
Reykjavik contains about one day's worth of entertainment. This is where the whale-watching tours go from, and the puffin tours, which are worthwhile mainly if you're not planning to go to other puffin cliffs.
Things To Do:
---- eat at Bergsson Mathes in downtown, get the lamb.
---- there is a happy-hour app, which you might use, because beer is $10-$15 a pint otherwise.
---- Fish restaurant is pretty good, also.
---- the good cafe is called Reykjavik Roasters.
---- buy some groceries from Bonus, it's much cheaper than eating out. Lamb is $14 for a leg.
Cars are how you will get around, unless you are a Tour Bus Person.
If you're comfortable with a stick shift, rent a yaris from Sadcars - about €110 for two days and ~$65 per half-tank of gas, and a half-tank is all you will really use in a day of driving. Gas was $2.25 a litre in July 2015. If you need an automatic, they're available, but cost more.
Get the gravel insurance. Icelandic gravel is unexpected, everywhere, and brutal.
Go to Vík
Vík is only 2.5 hours' drive from Reykjavik and there are a number of beautiful - like, unreasonably beautiful - waterfalls on the way, including Skogafoss. Also on the way is Dyrholæy, the big stone troll arch, and Reynisdrangar, which are a cathedral of columnar basalt cliffs. Vík itself is also beautiful, mainly for the famous black-sand beach.
Small Towns: Hveragerði of the Ground Farts.
On the way to Vík is Hveragerði, which has a hot river. You can take a hike up it and nap in the moss. The geothermal springs at Hveragerði are largely gone now - an earthquake did them in - but the volcanic molasses bread ("nature's own Dutch Oven") is quite good.
The Golden Circle
The Golden Circle is the equivalent of spending a day at the Louvre or going to a special exhibit at V&A elsewhere: beautiful, packed with tourists, has the best gift shops. You're already doing this, or you're not seeing the geysers. Stop in Alafoss on the way to Thingvellir and look at the actually-cool shops, particularly the knife-maker's.
Try the blue mint chip ice cream at Geysir. It's delicious even if you don't normally like mint.
Snæfellsnes Peninsula is where all your scenery ran away to.
There's very little in Snaefellsnes except horses, farms, horse-farms, rogue sheepsies, horses making more horses, and the best mountains and waterfalls anywhere. It is unreasonably pretty.
Borgarnes' Saga Museum has one of the better restaurants in west Iceland attached. The museum also contains a Scorn Pole (unsettling) and the saga of Eoill (ale, a big jerk). The restaurant's prix-fixe menu is great.
Further along by two hours is the small town home to the witchcraft museum, with famed latex model of necropants. Nearby is cafe Riis, which is pretty good. Get the fish soup. Always get the fish soup.
Basically, as long as you love road-trips and walking around near Scenery, you're set.
Enjoy your trip!