Even though Christmas is a very family oriented holiday in Iceland there's still loads to do :) Beware though as most Restaurants, bars and shops are closed on christmas eve and christmas day. Surviving Iceland recommends:
1) Getting cosy with an icelandic family that is open enough to let you in on their own family christmas. You REALLY have to play the pity card here if you want to get in, because icelandic people tend to be very private when it comes to their christmas celebrations (especially christmas eve). Pick the most vaulnerable family member and talk about how you miss your family and that spirit of christmas that only comes with being in a festive home with good people. Be very sad...very very sad, and you might just get lucky :)
2) Instead of putting in all that work to make a family take pity on you...why not
pay them for the invite? It might cost you a few ISK but you'll get a memorable experience out of it. Anyway it makes a good story when you get back home :)
3) Go to one of the few open restaurants in Reykjavik and treat yourself to a really nice christmas meal, wine an all. You'll probably meet some other travelers this way and hopefully make some new friends. Here's a
list of Restaurants that are open during christmas.
4) If all else fails: Buy a bottle of Brennivin and walk up and down Laugavegur getting drunker and drunker with each step you take. Practice the ancient icelandic walk:
Hunched shall you stroll with bended kness while calmly and carefully examining the nature of icelandic soil.