Forgot to mention, I also did a little research on getting from Reykjavik airport to the hotel (in case Regent doesn't choose to get us there). The Flybus works fine (we used it last time we were there) but depending on your hotel you have to go to a central terminal and then transfer to a smaller vehicle that takes you to your hotel with stops along the way. Since the Grand Hotel (if that's what Regent is using) is a ways from downtown, you would have to transfer. You can also get a private van for 6 or 8 that costs about the same per person(14,900 ISK total) through Private Shuttle that will take you directly to the hotel or you can just get a taxi that holds 6 people for about the same or a little less than Flybus (12,000 ISK for 6 people, 10,000 for four people). You'd need to book the Private Shuttle in advance, but the FlyBus and Taxi you can arrange when you get to the airport. You have to buy the FlyBus ticket at their kiosk when you exit the airport. All this information is on the Keflavik Airport website in the Transportation area (at the top of the website www.kefairport.is ). Click on the little British flag on the upper righthand corner or you'll probably have a hard time reading the information.
Private Shuttle and the taxis will also do city tours or other tours before you go to the hotel if you want.