Driving is the best way to explore the natural wonders of Reykjavik. Rental cars are readily available and can range from 4000-12000 kr depending on car type and time of year. Expect to spend around 2 hours driving for both day trips.
If you have more time, consider visiting other natural wonders within driving distance such as the Skaftafell National Park or the Jökulsárlón Glacier Lagoon. If you have less time, prioritize the Golden Circle tour but cut down on the number of stops at each location. Also, consider visiting the Reykjavik Botanical Gardens or watching the Northern Lights.