I've been twice and I plan on returning.
Highly recommended (spelling might be wrong, I'm doing this based on memory and my lack of Icelandic skills lol):
Hveragerdi: Hike to the hot river! It's a 60-90 minutes one way, kinda steep at first but easy trail. The river is really nice to hang out in and gets hotter the further upstream you go, so it works under any weather condition. And it's FREE.
Glymur: AMAZING hike up to a stunning waterfall (Iceland's highest IIRC). You drive like 60 minutes from Reykjavik, through like a billion traffic circles, but the last leg of the drive is breathtaking and the hike is spectacular (and not too hard, steep in places though). I actually hiked up at 8 pm and returned to my car close to midnight this summer. It was awesome.
Seljalandsfoss: Really cool waterfall that you can walk behind. BUT: keep going along the path to check out a few smaller waterfalls and another that's hidden inside a crevasse. It's super cool in there.
There's another cool waterfall after a 30 minutes drive further east, forgot the name... but worth it. And right after comes a really cool glacier. And then, the black beaches close to Vik!
Unfortunately, I haven't been able to see the Iceberg Lagoon thingy yet but it's supposed to be stunning.
The Golden Circle is a cool day trip, too. Strokkur goes off every 7 minutes or so, really nice geyser.
Also, while driving, pay attention to the signs with the little "circle squares" (no idea what to call them, but they are this universal symbol for cool shit). Just follow them and you're bound to see some cool stuff at the end of the road, be it cliffs, hot pods, or whatever.
Enjoy dude, Iceland is a very special place!
EDIT: Oh, and as for food: Bonus is the cheapest supermarket you can get. And their mascot is this weird little pig, love that guy. Don't eat out unless you have lots of disposable income I guess.