I did go. It was fab. But does she realise that around Christmas it will be pretty much permanently dark?

Best way is to fly - you can get some fairly cheap flights, then the bus goes from the airport right into Reykjavik.

I was attempting to minimise costs so was staying in youth hostels - the City hostel is actually quite nice, though it gets booked up quite early for busy times.

There's a Reykjavik tourist website that seemed quite good, information-wise, can't recall addy offhand but I'm sure it's googleable.

if you want to know more, just ask.