We went to Iceland in June of this year on a home (and car) exchange. $0 for room and car rental makes a big difference to the budget! But yeah, sticker shock. $30 for a (nice but not special) burger and fries. $10-12 for a beer to go with that. $6 for a Coke (but it was half a litre). $7.50 for a gas station chicken sandwich.
In some ways the best value was at the middle-to-high-end restaurants. We had a couple of $100 tasting menus that were on a par with what might cost $70 in France, so they were more expensive but not outrageously so. (But then we didn't have the wine pairings that we might have made in France.) At small places in Reyjkavik, the "fish of the day" makes for an affordable (though not inexpensive) lunch and is usually very good.
That said, we met some people who lived in Manhattan who said "Meh, it's only a little more than back home". And indeed, we went to NYC at the end of July and we didn't feel the need for cocktails outside of happy hour, once we'd added 27% for tax and tip. (Icelandic prices are all-inclusive, and there is no tipping culture, except in places that get a lot of Americans.)
There is an Icelandic airline called Wow Air that specialises in getting Americans to Europe (and vice versa) cheaply using Boeing 737s. Two four-hour flights and you've gone from London to New York with barely any less leg room than in cattle class on a 757. They have has fun with their aircraft registration codes, too: they have TF-MOM, TF-DAD, TF-BRO, TF-SIS, and (flying the San Francisco route, of course) TF-GAY.