Jökulsárlón is a must if you have ample time, it’s a 5 hours drive from Reykjavík but definitely worth the trip. Essentially large blocks of a glacier drifting down the lagoon into the ocean. I’ve been around but never seen anything quite like it.
Touristy yes, but worth it? Yes. You will usually find quite a few people walking up there but it's a great short hike and there is quite nothing like relaxing in the hot river before heading back down.
Skaftafell has a lot of great sights as it's surrounded by glaciers and volcanoes. Hike up to Svartifoss and even a bit further if you are up for. Recommend going on a glacier hike since you are in the area
A bit hard to get to but so so worth it. Don't recommend going if you are scared of hights but the view from above is something else
Mývatn is in the north on the other side of Iceland and has it’s own blue lagoon. The area is full of natural wonders and Dimmuborgir by itself would be worth the drive.
The old lagoon as the locals call but better known as the lagoon formerly known as the secret lagoon is a cool place to visit. Still not too many people there but really great experience and you can drink beer in the lagoon...
Hvammsvegur, 845 Flúðir, Iceland
The megaplex of tourism in Iceland but for a reason. Expensive as hell but still something you can't really miss while in Iceland. I would go later at night as there are a lot fewer people then.
Nordurljosavegur 9, 240 Grindavík, Iceland