From most major international airports in the United States (East Coast), you can get to Iceland for under $300-$400 one way. The quality of your trip depends on how much you're willing to spend, but in my experience, you can get a pretty cushy airplane ride for not that much money.
About The Airlines
Popular airlines that fly in and out of the area typically include WOW Air, Delta, Icelandair, and more.
Here's my experience with each airline.
WOWAir
WOWAir is a budget airline with direct flights out of Baltimore, Pittsburgh, Detroit, New York, and Boston. The airline is known for their fun, quirky marketing and signature purple branding. I've used WOWAir to fly in and out of Iceland from multiple cities. I've always had an enjoyable experience.
For instance, in May, you can book a one-way flight from JFK right to Reykjavik for $160, or $180 from Boston. Even Detroit is a steal at just $160 non-stop. The prices to and from the U.S. fluctuate in June - August, the tourist season in Iceland.
However, there are also a lot of cheap flights from Barcelona, Paris, and Berlin. Using Google Flights, it's easy to piece together a route that won't break the bank, and get you to Iceland quickly and safely.
Delta
Delta is another affordable option for travelers. We've all got Delta horror stories, but it's arguably one of the cheapest airlines to fly internationally. With Delta, you can fly from major cities again, with prices that rival Icelandair. They range anywhere from $250-$350 one way, depending on the airport.
Delta is also more enticing because of the upgrades. Passengers can opt for leather seats on Delta One (their dinner and a movie deal), or upgrade to Delta Comfort, which includes more leg-room, free snacks, etc. I'm still not a fan of Delta, given a lot of delays and cancellations I've had while traveling.
Icelandair
Icelandair is hands down, one of my favorite airlines to fly to Reykjavik. I don't know if it's because it's an Icelandic airline, but it just feels like you're already in Iceland, as soon as you step on the plane. You get comfy pillows, the seats are exceptional, and it's super easy to fall asleep. I don't know - it's always been my favorite.
I'd even fork over an additional $100 to fly Icelandair. That's saying something. You can get a roundtrip flight via Icelandair from JFK or Boston Logan International from $250-$350. The airline also offers a lot of flights into Europe.
The Airports
There's actually quite a few airports in Iceland, although you will very likely fly into Keflavik if you're heading to the capital. That's where the commercial flights go.
So unless you're headed to the Westfjords or Akureyri, there aren't a lot of good reasons to fly into the other ones. They're small, so the flights will be expensive and far and few between.
Here are the airports you're likely to encounter if you want to explore the country:
Keflavik
The Keflavik airport is 45 minutes away from Reykjavik. Repeat, 45 minutes away from Reykjavik. If it's at night, you won't be able to see anything outside the windows. So in the fortunate case that you're not driving, you may as well nap.
There's a few ways to get to the city from the airport, including:
Shuttles (my preferred method)
There are shuttles that go back and forth, but they are $20 each way. Most are extremely nice, and offer Wi-Fi that may or may not work. I've had it both ways.
City Bus
There are also buses you can snag at certain times of the day. You'll be at the mercy at the bus schedule for this one. They're pretty prompt. Many will route you through the main bus station right outside of the city.
Rent a Car
You can always rent a car at the airport. I've never rented a car in Iceland, though I'd really like to one day. It's just really expensive.
Cab
Don't do it. Cab fare in Iceland is outrageous. If you're even considering this, take the shuttle. Take the g'damned shuttle.
Reykjavik City Airport
Not the same thing as Keflavik. The Reykjavik Airport is mostly for internal flights, either within the country to Akureyri or Ísafjörður, externally to Greenland. The airlines include Air Iceland Connect and Eagle Air. The tickets range depending on locale.
Akureyri
Akureyri is - you guessed it - the airport that caters to the second largest city in Iceland. The airport will very likely fly from Keflavik, or connect through Keflavik if you're flying to Akureyri from another country. So if you're in Reykjavik, that's your best bet for flying there.
The airline they use is called Air Iceland Connect, and ranges from $100-$150 from Keflavik.
I'd highly recommend going to Akureyri. It won't be as touristy, but there's still a lot of really great things to check out, such as the Icelandic Aviation Museum (at the actual airport, too!) and the Akureyri Art Museum, or even the botanical garden.
Ísafjörður
Ísafjörður is located in the Westfjords. I may recommend flying there from Keflavik if you find yourself on a shorter trip. Otherwise, it'll take a drive from the city and a ferry to get there. Ísafjörður is absolutely worth the trip. The small town is breathtaking, and offers a lot of awesome activities such as whale watching, kayaking, and more.
There's also this neat Airbnb bookstore that you can stay at. Same as Akureyri, you can get to Ísafjörður via Air Iceland Connect from Keflavik or Reykjavik airports.