Here are some of the most memorable places we saw in Iceland. These are all towns or regions, so not specific beaches or museums. Each offers opportunities for you to explore, and make your own memories!
They are in counter-clockwise order, heading out of Reykjavik. Here’s a map:

1. Westman Islands
Very few tourists make it to the Westman Islands, a small inhabited island a few miles off of Iceland’s south coast. (The island is actually called Heimaey, and it’s just one of the islands that makes up the Westman Islands archipelago. But people use “Heimaey” and “Westman Islands” interchangeably.) About 4,000 people live on Heimaey.
On January 23, 1973, a volcano called Eldfell erupted on Heimaey. The island was quickly evacuated; by a stroke of luck, poor weather had caused the entire fishing fleet to stay in port, and these boats were used to evacuate residents to the mainland of Iceland. No one was killed.
But the eruption lasted for 5 more months. During that time, a third of the houses on the island were destroyed. Another third were damaged. Stop and think about that– two thirds of all of the houses on the island were damaged or destroyed. High capacity water pumps were brought in to cool the encroaching lava and save the town’s harbor.

There’s an aquarium that often has a pet puffin, a volcano museum that shows a house excavated from the lava, several nice restaurants hiking trails over lava, and more.

Getting there: You’ll need to take a ferry ride; in nice summer weather it takes 35 minutes. In bad weather or in the off season, it’s close to a 3 hour ride from a different port. I think it’s only worthwhile in the summer. See all of the details in our guest post about the Westman Islands (or in our book!)
2. Djúpivogur

Djúpivogur seems like the “right sized town” to me. That doesn’t seem fair, since other people might think bigger or smaller towns are the right sized. But we enjoyed exploring, let the kids wander by themselves, and had a great time.
You have the egg sculpture by the harbor, Eggin í Gleðivík:

And you have cool handmade stores, like JFS Handcraft:

Getting there: It’s right along Ring Road (Route 1), if you’re circumnavigating Ring Road. A great place to spend a night.
See a little more in our Live Iceland posts: Djúpivogur with eggs (written by my son) and Djúpivogur with JFS Icelandic Handicrafts
Seyðisfjörður

Seyðisfjörður almost doesn’t look real. Head over a steep curvy mountain pass. Keep winding around, and eventually you start heading down hill. And all of the sudden, Seyðisfjörður just appears before your eyes. It’s like a mirage after the mountain pass, but it’s real. You can be forgiven for thinking a place that looks like this doesn’t really exist.

But it does, as does the wonderful Tvísöngur sound sculpture. Hike up the hill and … sing! Each dome resonates at a different frequency.

Getting there: It’s about half an hour each way off of Ring Road in East Iceland, over a mountain pass. I loved the drive (and seeing snow up there at the end of May!) but you’ll need to take it slow in some places.
See more details in our live post about Seyðisfjörður:
Ísafjörður
We’re up in the Westfjords now … I don’t think it makes sense to try and get to all of these places unless you have over a week in Iceland!

Ísafjörður is the largest town in the Westfjords, but it still isn’t big: 2,600 people or so. But you’ll find the wonderful Gamla Bakaríið (bakery) and the unforgettable Tjöruhúsið fish restaurant:

Those are regular sized spatulas in a gigantic pan. It’s an incredible experience. And if you have kids, it’s one of the best deals in Iceland– kids 14 and under are free!
See our post about Ísafjörður:
Hellnar and Arnarstapi

Okay, this is really two towns in West Iceland, on the Snæfellsnes Peninsula. But they are connected by a magnificent seaside hiking trail. Start in Arnarstapi (or don’t … it doesn’t really matter). In Hellnar, you’ll find a cute cafe; get a meal or just some hot chocolate before heading back.

Reykjanes Geopark
The Keflavik airport is almost definitely your entry and exit point in Iceland. It’s on the Reykjanes Peninsula; many people skip the whole Peninsula and head straight to Reykjavik. But they’re missing out on the Reykjanes Geopark. It’s full of beautiful lakes:

A fun geothermal area, Seltún-Krýsuvík:

And a Bridge spanning two continental plates.

What did I miss? What were your favorite spots in Iceland?