Hi, thank you! The summertime is a good time to visit Iceland, I would recommend you to go to The BlueLagoon, I recommend to do that for one day and then to explore the downtown Reykjavik after that. Thingvellir (Þingvellir) the national park, Gullfoss and Geysir is one day trip. You can take a tourist bus or rent a car.
If you are interested in hiking I recommend the walk from Skogar (Skógar) to Thorsmork (Þórsmörk), the walk is around 30km and you can do that over one or two days. On the way you see lot of beautiful waterfalls (around 50) and incredible landscape. And it’s nice to stay in Þórsmörk and hike around as well. It should be possible to rent a car or take a tourist bus. You should be careful driving over the rivers in Þórsmörk, they can be dangerous.
There are so many places to see in Iceland and enjoy so you should plan the trip and what you want to see. If you want some other recommendation just let me know. =)