Sorry if this is too late but...
Best chance of seeing the lights is from the plane if you are arriving at night. Otherwise, take a stroll along the seafront in Reykjavik after dark and look out over the mountains and you may get lucky.
As for activities, you should do the Blue Lagoon and the Golden Circle (either classic or express). These are both booked from the hotel lobby - ask for the Iceland Excursions tour for the better rates.
If you only do one tour, do the Golden Circle. To save time and money, you can replace your returning airport transfer for one which includes a visit to the Blue Lagoon. Ask at the hotel lobby for the "Blue Lagoon and Keflavik Airport" tour. These are really good value and make for an excellent end to any visit.
In Reykjavik, take a stroll up Laugavegur, the main shopping street, and go inside Hallgrims Chruch, Reykjavik's Lutheran cathedral and its steeple (Reykjavik's tallest building).