I think @PLee is confusing Sky Lagoon, which is on the outskirts of Reykjavik, with Blue Lagoon, which is near the airport
2 full days in Iceland? I'd book the Blue Lagoon for arrival day and use their transportation to get you from the airport to the Lagoon and on to your hotel. And on the 6th I'd take a Golden Circle or South Coast tour with a local provider. Reykjavik is a cute city, but the nature in Iceland is spectacular, and you won't really see it in the city or at Blue or Sky Lagoon (which are both great).