Some advice from a native Icelander:

3 Frakkar is a must. If you are an adventurous eater, I recommend the smoked puffin tartare and the whale steak. If not, their twist on the traditional Icelandic "plokkfiskur" fish hash is not to be missed.

Forget Perlan. It's a tourist trap of the worst kind, and since the economic crash seems forlorn and abandoned most days.

Laekjarbrekka is a more traditional choice but no less delicious. If they still have it on the menu, the lamb/langoustine "surf and turf" option is amazing.

Silfur at the Hotel Borg is a bit more modern and trendy in both decor and cuisine, but both meals I've had there were amazing. Their "lobster three ways" is a must if they still have it.

I hear good things about Dill, which I have not been to but all my friends rave about.

There are also some excellent ethnic restaurants. Austur-Indiafjelagid offers great Indian food and there is a fairly new Nepalese restaurant (can't remember the name) on Laugavegur. For old-time Italian, restaurant Italia is decent.

On the lower end: Icelandic Fish and Chips is fairly self-explanatory, Saegreifinn has wonderful seafood, and you absolutely must stop for the famous Icelandic hot dog at the downtown Baejarins beztu pylsur hot dog stand.

For snacks, I recommend visiting our bakeries. We have amazing pastries, both sweet and savory, and they make for wonderful between-meals filler.

Enjoy Iceland, and spend some money - we need it!