I would recommend the Westfjord area. It is located in the northwest of Iceland and is off the main road that goes around the country. There are still some tourists there but nowhere near the amount you get in other areas. It also has some stunning nature views if you know where to find them. The Dynjandi waterfall is located in that area for example.
Then there is Melrakkasletta, which is the most barren wasteland you can find in Iceland. It is a small peninsula to the north-east about as far away from Reykjavik as you can get. You might come across the few people that live there, but the chances of finding tourists there is slim. The offset is that, in my opinion, there is really nothing interesting in that area.