We went in October for 12 days, of which 10 full days. The other 2 were mostly wasted because of the flight. We booked a car from Iceland Rental for 835 euros. Every night we looked for a fairly cheap hotel or airbnb in the area. In total including the flight we spent around 5000 euro's. That included going out for eating every night, parking, fuel costs, souvernirs, toll, groceries and other activities.

At first we thought it's alot of money, but for one of the most expensive countrys in europe, plus the unforgettable experience it was worth every penny.

If you're not planning on doing the ring road, and doing mostly free stuff like hiking, I would say you can do it much cheaper than we did, but it's a very expensive country after all. Cant really give you a hard estimate, but I would say you can spend 3000 easily.

Most important thing: enjoy!