Getting To Reykjavik
Iceland Air is a fine airline… nothing special, rates are best in the offseason (spring & fall), summer and winter get expensive… We flew for ~$800 RT from JFK in the highest season (late June, when the sun never sets) . Unfortunately Iceland Air is NOT a global airline partner, but you can use Amex or Chase Points to offset the cost, or transfer in SPG.
WOW is the hot airline of the moment since it's super cheap and even flies direct from Los Angeles… we haven’t heard much about the experience beyond it being a no frills airline that gets you there. Word to the wise, deeply discounted airlines that fly once or twice a week can end up really messing up a vacation in the event of a significant delay or cancellation.
Delta also flies to Reykjavik direct — and it's a good way to use Amex points if you have them available to transfer.
DO NOT book a taxi or private van from the Reykjavik airport, it's a total waste of money. Use this Airport bus instead, it's super cheap (~$25 each way). Reykjavik is TINY: Fly bus company can drop you off and pick you up directly from your hotel or apartment. They even have wifi on board, so you can be instagramming the midnight sun from the moment you land. Here's the link: http://www.airportexpress.is/default.aspx?AffiliatePass=fa43ee95-8ed4-40ae-9e97-170513a815c3
Staying in Reykjavik
Again, Reykjavik is tiny -- so most hotels and apartments will be well situated (unless they are way out of town). Many people avoid Reykjavik all together and go to other parts of the country... we have yet to do that yet, but it's on the list.
For a larger group, we recommend staying at an Airbnb like this one that we enjoyed: https://www.airbnb.com/rooms/654610 the host Maria was great, it was literally perfect location on the main street (Bankastraeti) and it was a huge apartment that could easily sleep 10-12 people.
A hotel we found that we would highly recommend staying at is KEX HOSTEL. It's a fantastically designed old industrial building down by the water, that features cool people and an amazing bar scene: http://www.kexhostel.is
Eating in Reykjavik
GRILLMARKADURINN - Before our trip, this was the top recommended restaurant in Reykjavik that people were talking about. I must say, it didn't disappoint - the food (Scandinavian style grilled meats & foraged veggies) was fantastic We had whale and puffin! But there is a caveat here -- we went as a group and pre-negotiated a ~$75/person tasting menu. This DID NOT included booze, which we added on three glasses (wine, beer, well mixed drinks) per person for an additional ~$30/person. The total ended up being a completely reasonable ~$105/person for an amazing 6-course tasting menu + alcohol, but again, this was NOT on the menu. We pre-negotiated by reaching out ahead of time through the website - suggest you do the same.

Saemundur (Kex Hostel): This amazingly inexpensive restaurant in the hip lobby of Kex Hostel (see above) serves high end bar food prepared by the same chef who runs Iceland's top restaurant (DILL - we didn’t go here, you need to book way in advance)… this is apparently his “low key” spot. To be honest, it was probably our favorite meal of the trip and with a couple of great beers each, it only cost ~$35/person (everything is a la carte). It's also the best place to meet other interesting travelers, with a laid back atmosphere complete with communal tables...where you can sit and enjoy the midnight sun traversing the sky across the bay out your window.

FISKFELAGIO — You can't come to Reykjavik without going for seafood, and this place we believe is the top fish restaurant in Reykjavik. Similar to what we did at GRILLMARKADURINN we set up an Icelandic seafood tasting menu (~$75 each for tasting menu + ~$30 for three glasses of alcohol). Amazing deal when you consider the quality of the food...which was absolutely ridiculous.

THE COOCOO’S NEST (BRUNCH/BFAST) — This is hands down one of the best breakfasts we have ever had. The Coocoo's nest is a bit tough to find, as it's down by the docks in what looks like a parked shipping container. The interior (above) is Scandinavian design to the max, with a fun bar to sit at while they prep your food just a few steps away. There is often a line out front, so we suggest going EARLY or on a non-weekend day... the breakfast plates are ENORMOUS, the pancakes and sandwiches were out of this world. You would be a fool to miss this place!
PRIKIO (BRUNCH/BFAST) — It's kind of hilarious to think back about this place, because at nights this is the hard core "hip hop" bar… but they actually serve an incredible breakfast/brunch… It was right underneath our AirBnb (see above) on Bankastraeti in the heart of town, and for ~$12 you could leave full on eggs, bangers & mash, grilled peppers & tomatoes and never ending coffee refills. It's one of the best deals we've found while traveling.
Going Out in Reykjavik
DON'T DO THIS -- Avoid the bar crawl, and any of these 'bachelor/bachelorette' party specialists running around claiming to be nightlife experts. As a general travel rule, don't go anywhere they are handing out drink tickets. Our advice, skip the clubs (or maybe go one night just to see it), this includes B5 & Austur. If you're dead set on trying one, B5 (the 'hippest club' which is literally a pizza place that turns into a 'club' at nights) is at least a fun place to people watch. A word to the wise though, no one is going to be impressed by buying a table. This is an egalitarian Scandinavian country... you actually lose credibility here doing things like that.

End your afternoon, start your night (feels the same anyway when it's light 24 hours) every day, every night, here: Mikkeller & Friends (Pictured Above) — this spot holds a special place in our hearts, as we have now been to the outposts in Copenhagen, Stockholm, San Francisco and Reykjavik. It is the absolute best place to wind down from a crazy active day, with an endless chalkboard of INCREDIBLY interesting beers and great bar snacks. You will meet very cool, interesting people here as well… it's a true hidden gem that is not to be missed.
Hurra — Hands down the best bar in Iceland… It's the only actually cool/authentic place where people go to party, and not just be seen. When we went it was all LCD Soundsytem type music, no top-40. It's Scandinavian grunge at it's best, and it's a great place to dance and party and not feel like a tool bag visiting Iceland in a V Neck and Blazer (shout out to the Long Island kids we saw at B5). The real locals recommended this place to us, and it's the only true nightlife spot we would return to.
Doing Cool Stuff in Reykjavik

GLYMUR FALLS HIKE: https://guidetoiceland.is/connect-with-locals/jorunnsg/hiking-to-icelands-highest-waterfall---glymur This is a truly amazing hike that starts in tundra and then enters a canyon that feels straight out of Jurassic Park. We rented a car (~$75/day including gas from Hertz) and drove 90min out of Reykjavik to make it here… The hike itself took about 4 hours total. Definitely bring hiking boots, as it's a steep and wet climb. When you reach the top, you have the ability to take off your boots (and socks) to cross the river that feeds the waterfall below. This was one of the most painful, cold, amazing and most memorable experiences of my life… It’s the only way to get down the other side of the trail and the water is 33 degrees. It's not a soft flat stone river bed either, we are talking about 50 yards of jagged volcanic rock. Once you hit the other side though….your feet have literally never felt better, and then it feels like heaven/walking on clouds the whole way back down.
RAFTING: http://www.adventures.is/iceland/rafting/riverfun/ — These were by no means the craziest rapids (class 2-3), but it was a genuinely fun day with friends. The landscape is magnificent, as a fun activity - you can throw your friends overboard and dive in too… the scenery is some of the best we've ever seen out on the river.

MOUNTAIN BIKING:1,000 Rivers Road (http://goo.gl/HQNjt1)
This is a demanding (4 out of 5 difficulty) mountain biking trek, that includes stops at geysers, volcanic holes and hot springs… this is a full day trip. It cost ~$230/person (includes transit) — and it was absolutely worth it. It's also, completely insane. We all fell a bunch of times (mostly, thankfully into the mossy ground that covers the volcanic rock). The hot springs come at the end, when you are beat up and exhausted and they are so cool. Imagine a little stream in a green mountain side that happens to be 99 degrees Fahrenheit. This is an activity where you will get dirty and a little banged up, definitely not for the faint of heart, but don't be scared either... you will earn your beer!

HIKING: Fimmvörðuháls Volcano hiking trail (http://goo.gl/2hE4qh). 13+ miles, 10+ hours — experienced hikers only, this is an intense day hike that is consistently rated as one of the most beautiful/incredible hikes in the world… not every day you get to hike up live volcanoes. At~$250 - $350/person (including transit, poles/gear, guide, food) it ain't cheap either.... but IT. IS. WORTH. IT. If you love to hike, do not skip this...
Skip this Stuff in Reykjavik
The Blue Lagoon is a tourist trap and a complete waste of time & money, it’s not even a real natural phenomenon… it’s a big fake giant luke warm hot tub full of tubby Europeans on lay-overs.
ATVs & Snowmobiles are not exactly our thing, as we'd rather be the ones doing the moving than being moved… but if they are your thing… go for it… What we will say though is that this is an activity you can do in most winter adventure towns. The big issue is price... Reykjavik based adventure tour companies charge massive premiums... so why not just save the snowmobiling for Canada or the US?
Golden Circle tours… there are A LOT of tour groups offering trips to all the "top sites"… But just imagine sitting in a jeep all day as you drive from one tourist picture spot to another. No offense, but this is essentially the 'segway tour' of Iceland, something for sedentary people to feel like they did something 'adventurous'… Sure it's a quick way to see the most spots that are in the post cards… but literally EVERYTHING in Iceland is otherworldly, so wouldn't you rather hike or bike or raft to it instead? That's just our belief... but yours may differ, and that's cool too.