Consider renting a car to fully explore the stunning nature Iceland has to offer completely at your own pace. The sights listed can be visited on a day tour easily, however. The estimated cost to rent a car for the day is around $100, while a day tour will set you back around $130-$150, but it includes admission fees and round trip transport.
If you're willing to extend your trip beyond a single day, consider adding an additional day to visit the otherworldly geothermal area of Geysir and Strokkur's eruptions, which are also situated in Thingvellir National Park. For the more adventurous traveler, going out to see a whale or other native wildlife could also be considered. If you have limited time, removing Laugarvatn Fontana may be necessary, but we wouldn't recommend it.