They are typically clean, but as the other poster mentioned, they are very basic. I found a few to be a bit worn but fine overall. The only nice hotel I stayed in on the road was in Hofn - Fosshotel Vatnajokull. The rest were basically hostels with private rooms; bunk beds, some shared bathrooms, even an off season boarding school.

But everything was functional and clean. Most of the sights around Iceland are free so not many tickets to take care of. I just got back last month from Iceland, we just rented a car. I made hotel plans beforehand so it was easy enough to plan each day. Self driving is very easy as there is basically just one main road and everything is well marked. Google maps works well too as backup.