Our family of four visited Iceland in June 2023, and here's a few thoughts/highlights:
We landed on a Saturday, did the Blue Lagoon the morning we landed, and headed to Reykjavik for one afternoon and evening. I liked Reykjavik more than I expected. It's central area is buzzy and it was fun to see the Phallological Museum (with an excellent cafe with waffles shaped like you know what). A wonderful, small food hall (Hlemmur Food Hall) is worth checking out for dining options. Center Hotel Laugavegur is an excellent, central option (and reasonably priced by Iceland standards - 2 double rooms for 525 euros total for one night). I would have liked another day in Reykjavik.
As expected, the Blue Lagoon is pricy, but we found it worth it. It's massive, and a very unique experience. We also swam in heated pools at a local aquatic center in the tiny town of Hvolsvöllur (near where we stayed) for a completely different, more local and much cheaper experience. There we met the director of the aquatic center, who told us that (a) he was a waiter at the hotel where Secretary of State George Schultz stayed when Iceland hosted USSR and USA peace talks in 1986, (b) that it was Iceland's female leader's calming presence that led to the breakthrough in the conference / cold war, and (c) that the greatest American hero is Bugs Bunny. You won't meet that guy at the Blue Lagoon.
We were based in an AirBnb near Hvolsvöllur most of the week. Selfoss, Hvolsvöllur, or Vik would each make excellent towns for South Coast home base (Selfoss and Vik are each more attractive than Hvolsvöllur which is just functional).
We liked Vik a lot and visited twice. It's small, but very close to Reynisfjara (famous black sand beach) which is windy and wild. Vik has a gorgeous setting and a few small restaurants worth checking out (we enjoyed The Soup Company for lunch and Smiðjan Brugghús for beers/burgers).
Selfoss is a little bigger town, also with a nice food hall near the center (in an old but nicely refurbished dairy barn) and a charming square of refurbished (colorful) buildings outside.
Jökulsárlón National Park has a glacier lagoon (a couple of them I think), and this was one of the highlights of our trip. It's a long way there (3 plus hours one way from Hvolsvöllur). If you can get to this glacier lagoon, it's really amazing. There's a black sand beach just across the road, and it has chunks of glacier ice sparkling in the black sand (hence the name Diamond Beach).
Our favorite day out was a ferry trip to the Westman Islands. The ferry port is near Hvolsvöllur, and takes 45 minutes to carry you (and your car if you wish) out to the island. The town of Heimaey is the only real town on the sole inhabited island, but it was the most charming of any of the towns we saw. The island has 2 volcanos you can climb, each about 45 minutes or so (no lava bubbling up or anything like that). We climbed Eldfell, which is the volcano that erupted in 1973 and caused evacuation and massive damage on the island. It helped that we had sunny weather for this day trip - that is very uncommon for this island (even less common than Iceland in general).
The waterfalls are amazing. They are everywhere. And some of them are inundated (in June) with tour busses and people. Gulfoss is massive, but probably had 20 tour busses there when we visited. We loved Skogafoss. This was about 20 minutes drive from our AirBnb. We went two separate nights, at 10:30 pm (light out all the time in June), and the place was magical. There were people but not crowds. The point is that we loved Iceland's natural wonders, but we are not alone in that and it helps to visit popular ones early or late or to just pick random ones (there are sign posts along the road everywhere) and just take a chance on something less well known or that requires a hike to get to. For example, we found Porufoss was a favorite and we were there alone.
It was a great trip!