Here is a 4 night 5 day Itinerary for you. Well, we technically made it 3 nights and 5 days and just didn’t sleep a day :)
Rented a car from one of the many options near the airport. When we arrived the airport is swarming with different shuttles taking you to your car rental location, be sure and give your location a call and they will shuttle you to your rental area. Tip: be sure and get a all wheel drive or four wheel drive. This so important especially in the winter in Iceland. When you hit your first Iceland winter storm, you will be thanking us!
(Note and warning: we hit the craziest winter storm of our lives! Both J and I grew up in Michigan so used to crazy storms. But between 50 mlp hour winds, snow, sleet, complete darkness and a complete white out… oh and in mountains we’ve never been in! It was the craziest drive our life but made it to VIK but this did take from our time and had to reschedule some things!)