When you arrive in Iceland the shuttle to The Blue Lagoon awaits just outside the terminal. Swim around in the lagoon as long as you want and you can have a cold beverage from the bar, too. When you feel fresh and warm it is time to get back on the shuttle into the city and you hotel. Use what is left of the day to explore the charming city.
Depending on your arrival it might be enough time to go on a whale watching boat tour from the old harbor. You can have a look at the excursions here.