Wow! Iceland is really for the outdoors ... for a short trip the Golden Circle is a must. But you are facing limited daylight hours, and possibly bad (windy) and cold weather so don't self-drive ... take a tour. You could also visit the local swimming pools if you don't want to stump up for the Blue Lagoon. Remember that Iceland is very pricey ... your flight is probably the cheapest part of your trip! The local newspaper (available on the internet)
The Grapevine (
https://grapevine.is/) gives listings of restaurants and happy hours.