The quick answer is ... that there is no quick answer (in my opinion) because you can do Iceland for a lot of money and you can prepare and do it for less.
If you take a look at the accommodation options the price differs greatly between season and type of accommodation. If you look up prices of 4* hotels in Reykjavik City Center during July you will be looking at 300$ for a twin/double [at the time of this post] which we can all agree is pricey but probably will only go up from this post.
If you are travelling more than 2 together I would seriously look into booking an Air bnb flat. For around 3-400$ you can get beautiful flats (will come to the food prices later) with kitchen - which will cut the cost of food. If you are travelling by rental car it is not necessary to stay close to the city center. If you will doing day-tours (e.g. www.icelandtrip.com ) it is so much better to stay close close to the city center since pick-ups from hotels/hostels/etc are so much more accessible that way. Cheaper options are available at Air bnb and in general Icelanders are good hosts 🙂
If you are staying at an Air bnb you want to go few times out for a dinner/lunch but rest of the time stay at your flat and make dinner. Hers is a trick and that is to buy prepared seafood courses at www.fylgifiskar.is which are ready for the pan/oven. They have a couple of places but the one at Borgartun 26 is closest to the city center.
If you want to buy groceries there are two groceries stores that are considerably less expensive than others, www.bonus.is and www.kronan.is. Do NOT buy your snacks, groceries, drinks, etc., at corner shops or gas stations.
And be prepared before hitting the road for your full-day nature sightseen and make your lunch/snack before departure. You will thank me 😉 and it is no lie - the water is perfectly healthy straight from the tab so do NOT buy bottled water (or maybe once and re-fill it yourself).
Here is an important point, buy alcohol in the duty-free store at arrival. If you don´t your second best option is www.vinbudin.is, which is a state run alcohol store. Alcohol at the bars can be ridiculous expensive but you can check www.happyhour.is for deals - but "for some reason" they only have their website in Icelandic but you should be able to figure out what each place have to offer.
Now coming to the important part and that is the reason you are thinking about coming to Iceland - The Nature. Still, the access to the most popular tourist attractions are free. Doing the Golden Circle, The South Coast, The Ring Road or just anything that only requires your eyesight will not draw you back about anything more than getting you there. If you are travelling via car most of these common places are very accessible during summer time but during winter time it is always question about the daylight, the weather and how heavy the snow has fallen until your visit.
Regarding car-rental prices and gas - those things are relatively more expensive than in many countries and when adding "Sand & Ash Protection" and "Gravel" or "Windshield" insurance or even greater insurance since (let´s say it like it is) the roads in Iceland are not in the best condition ...
If you rather like to explore Iceland´s nature as a part of operated tours we certainly can point out a few options that does not take up all your budget.
Golden Circle Afternoon for 9,900 ISK (~87$ at time of writing) and Golden Circle Classic (~92$ at time of post) 10,500 ISK. If you find these (or similar tour) for better price we will certainly try to match the prices but this should be as cheap as the come.
South Coast and Waterfalls 13,900 ISK (~123$ at time of post) and The Beautiful South Coast 13,400 ISK (~118 at time of post) are among the least expensive South Coast tours we are able to offer. And again, if you find these (or similar) tours on the south coast for less - let us know and we will try to offer same tours or try to match the prices 🙂
Northern Lights Bus 6,400 ISK (~56$ at time of post) we believe is the least expensive way to see the northern lights - we have not come across less expensive tour but correct us if we are wrong.
It is also worth noting (and often forgotten when comparing Icelandic prices to some other countries) that tax is included in all reported prices so you cannot expect you prices to increase at the check-out. It it also NOT required/expected of you to tip - but very welcomed for exceptional service. If you find the prices of (e.g.) restaurants is too expensive relative to the quality do not tip. Check out my post regarding Good Value Lunches for a quality lunch for under 20$.