I've been to Iceland 3 times. It was my favorite country to visit until the tourist boom began. Now I think I'll wait and see if things calm down before I go back. However, as noted by someone above, it's still not too hard to find off-the-beaten-path areas that are very impressive. For example, we got engaged at the base of the 3rd largest waterfall in Iceland, and there was no one around to witness it. :-)
I've done a G Adventures trip (meh, but enough to make me want to go back), a 6-night backpacking trip with a guide and two other people, and an 11-night Ring Road camper van trip with my now-husband.
I would actually strongly consider skipping the Golden Circle (unless you like looking at miles of tourist buses) and blasting directly past that and starting your trip with Vik and points east of there. In my opinion, while the waterfall is impressive, the rest of the Golden Circle isn't that great, and it's not worth the time if you have limited time. And the entire island is covered with waterfalls. I mean, so many that it became a joke for us. Rainbows, too. They're all fantastic, but that means it's okay to skip one.
Do not miss the shuttle bus from the airport to Reykjavik. Taxis are expensive. Ask me how I know. Do get your liquor (quickly!) at the duty free shop at the airport. Upon your return to the airport, leave yourself MUCH more time than you think you need. On both my 2nd and 3rd trips, I stood in line for over an hour (maybe two?) at the Delta checkin desk, just to check my bag. (I typically don't check a bag, but I was camping, so I had a lot of stuff.)
Reyjavik is a nice city, but it's very small. Unless you have some burning desire to eat at every restaurant they have, there's no need to stay for more than a day or two. I literally ran around the whole city in one afternoon; there's a nice loop for runners/walkers/cyclists. And yep, AirBnB seems to be the way to go for lodging if you're not camping.
Yes, Bonus grocery stores are where you'll find cheap food! And +1 for oatmeal! That was our daily breakfast. I also took along a bunch of dehydrated fruits, vegetables, beans, etc. to make meals when camper vanning. Oh, and we bought a lot of bread at local bakeries everywhere we went. We typically started our morning at a coffee shop so my husband could get his caffeine and we could use the Wifi, and we usually bought a loaf of bread to eat over the next couple of days.
If you eat cheese, you'll find that good European cheese is relatively cheap. Cheaper than cheddar.
For those renting a camper van, we found that the best way to stay clean was to make use of the public swimming pool (translation: pool that almost no one uses, with 2-3 hot tubs next to it that are the social equivalent of an Irish pub) in each little town where we camped. Even the tiniest towns have a swimming pool. It's something like $5 per person to enter, and you're required to take a (completely naked, in public, just get over it) shower in the locker room (men/women separated), and then you can enjoy the hot tub and/or pool, then shower again before you go. So you end up squeaky clean and relaxed by the time you leave. This was just last summer, post-tourist-boom, and we were still the only tourists in every pool (we didn't go to the ones in Reykjavik, though), so I think it hasn't quite caught on yet.
One other camper van tip that ended up working well for us: get a map. A real, paper, folding map. My husband gave me one that was something like 5x6 feet when completely unfolded, so I spread it out on the living room floor and had a blast marking spots that we wanted to see during our drive. I just used internet searches to come up with ideas. Not that we had to hit every one of them, but it gave us a really good idea of what was out there. That map ended up being on my lap for the entire trip, unfolded just enough to see the area where we were at the time. I like technology, but sometimes it's too much trouble. And yeah, there's zero need for GPS.
My two favorite, not-so-touristy parts of Iceland are the Westfjords:
https://www.google.com/search?site=imghp&tbm=isch&source=hp&biw=1280&bih=602&q=hornvik&oq=hornvik&gs_l=img.3..0l2j0i24k1l4.482.1464.0.1970.8.7.0.0.0.0.166.529.3j2.5.0....0...1.1.64.img..3.5.525.0..35i39k1j0i30k1.QY9ud6CJiLwand Seydisfjordur:
https://www.google.com/search?q=Seydisfjordur&site=imghp&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiL5L37jcPUAhUJ1GMKHQ-NBoIQ_AUIBygC&biw=1280&bih=602My 6-night backpacking trip was through the Westfjords, including Hornstrandir. Completely amazing. I did use a guide out of Isafjordur (cute little town, no need to stay more than a night, not much to do unless you're using it as a base for adventures), and I was very happy with them (boreaadventures.com -- family run, my guide was the 26 year old son of the owners and was more than competent). I've done a lot of hiking/backpacking in a lot of parts of the world, and that was one impressive hike. We were lucky to have incredible weather, though. If it had been cold, windy, and rainy the whole time like it was on our last two days, it would have been much less awesome. Even if you're not interested in hiking, just driving the Westfjords is worth doing. The rental car/van companies may try to steer you away from it because the roads are less great than they are elsewhere in Iceland, but they're not bad (as of 2 years ago). And there's a great campsite in Isafjordur (also nice hotels). Even the campsite has a waterfall view that would be a destination hike in most parts of the US, but in Iceland it's just "oh, by the way, there's another waterfall." Just from the car, we spotted a whale in one of the fjords.
Seydisfjordur has a nice little campsite right there in town, just across the street from a couple of small bars/restaurants. It's also where the ferry goes to/from Denmark. Near there are some nice hikes, too.
Iceland is a beautiful country. I have mixed feelings about being a tourist there. I'm happy to give my tourist dollar to a place with such beauty and such kind people, but I worry about too many people like me trampling that natural beauty and frustrating those who have lived there for generations.
