So you're tempted to go yourself? Wait until spring. More reasonable weather and the scales tip to favor endless daylight over pitch dark.
Flights
Iceland Air is your only choice and it's a good one. Nonstop from San Fran, Orlando, Baltimore/DC, Minneapolis, Boston and JFK. It's about 5 hours from the East Coast cities, 8 hours from SFO. Flights are around $500 to $600 R/T. If you're headed to Europe, they offer free stopovers for up to 7 days. If you're going to stay at a traditional hotel (vs. hostels, guest houses), you can save a meaningful 50%+ booking one of their packages. The airline owns 8 of the nicest hotels in the country.
Car Rental
We chose Budget. Hertz and National also are both there. It's going to start $200 per day no matter what you who you pick. We did fine with a Toyota RAV4.
Lodging
> Nights 1, 2 and 7: In REYK we stayed at the Butterfly Guesthouse (here) which we'd recommend again and again. They have rooms where you share a kitchen and bath or apartments with your own stuff. Very clean and a nice collection of other guests. The owners are terrific hosts with plenty of good advice. You're about 100 yards from downtown and still on a quiet neighborhood street.
> Night 3: In ARNES. Hostel with good hot tub, pool facility. (here)
> Night 4: In VIK. Small prison-width beds. (here)
> Night 5: In VAGNSSTADIR. Great sunroom. (here)
> Night 6: HVERAGERDI. Horse ranch. (here)
