Nothing to do at all but Keflavik hosts the international airport. If you land late, sleep there. It's much cheaper than in Reykjavik.
Renting a car at the airport is also cheaper. Do not pay 20$ more for having your car delivered in front of the terminal. All companies have their office in the area. After a 10min walk you will be at your car and you will have spared money.
NOTE that if you are travelling as a couple, it's still cheaper to rent a car! Buses to Landmannalaugar are expensive (90$/p).
A lot of tourists (I should say French tourists) do not pay for a 4x4 and rent a conventional car like a Toyota Yaris and are driving off road even if it's forbidden. You can do that despite tattling is common in Iceland, but you really won't be able to go everywhere. As the country is small, you may make a tour with a small car, go back to Reykjavik and rent a 4x4 for a few days. Off course this means more time spend in a car, but you will also see more for a better price. (I did so...)