I will only add -

The people are great, could not have been more friendly and helpful.

They all speak practically perfect English, because no one can speak their incomprehensible language of the Vikings, with 30 letter words. If you want to make them laugh, try to address them in phrasebook Icelandic. Better yet, lose the phrasebook because you won't need it.

The Old Iceland restaurant in the center of Reykjavik is superb. Yes, that's the name. It's a small place, make reservations.

The food is terrific, stay local, fish, lamb, etc. and you can't go wrong.

The pastry shops are nothing short of awesome. It reminded of the ones in Denmark (where "Danish" is called "wienerbrød" (Vienna bread)). And they have wonderful Danish or wienerbrød, or whatever they call it in Icelandic.

Beware of the wind on the drives on the southern coast road in places. It will knock you down.

We went in October- we wanted to avoid the crowds. Average temp was 30-40 degrees. It did rain a lot. Still loved it.

Recommendations
1. Wear layers. Bring rain gear, but not umbrellas- too windy.
2, We avoided booze...very expensive

The best stuff to see is on the ring that circles the island. Nothing much in the middle except mountains and glaciers. Therefore, renting a car is the best option. There is a lot driving involved. Reykjavík is where 75% of the inhabitants in Iceland live. It's a decent city, but you can see all you need to see in 1-2 days (at most). Plan on driving around the ring. NOTE: Bring a roll of toilet paper and be advised there are not a lot of restrooms along the ring.

Many people I know make the mistake of staying in Reykjavík over the entire trip. This will involve a bunch of inefficient driving back to Reykjavík every night.

Strongest recommendation: Identify all the cool stuff you want to see and plan an iteniary to stay in an AirBNB along the way. So you don't spend the entire trip driving. We went about 3 days southeast of Reykjavík and then came back and went 2 days northeast of Reykjavík and we ended the trip one night in Reykjavík . We did not have time for the northeast part of the ring.

Vik is one such town, about 2 hours from Reykjavík. From Vik, we went horseback riding along a volcanic black beach, and then drove over a glacier/ lava bed to some ice cave exploration. We all enjoyed this the most of the trip. You will need reseravations for these.

Other cool stuff:
1. The Blue Lagoon is the most famous mineral springs on the island, There are many more available that are cheaper, but we liked Blue Lagoon not just because it was a great experience but because to get there you have to drive over a lava bed from an active volcano (last erupted last year I think) and you will see steam escaping all over the landscape. Iceland is like another planet!
2. There are tons of excellent waterfalls! We identified about 20 along the way we were driving. Very worthwhile. My recommendation is to search "best waterfalls". At least one massive waterfall you could walk behind the falling water.
3. Incredible active geysers
4. Old shipwrecks/plane wrecks
5. There is a cool spot near Blue Lagoon where you can stand on a bridge that straddles the boundary between the North American and Eurasian tectonic plates (if you are in to geology)

Other advice:
Get the additional rental car insurance for a small price per day! Usually I would avoid this, but not in Iceland. We had a diesel car which I am not used to. At the end of the trip I topped of the car with normal gas because I was tired and it was confusing which hose was which. It cost me a few hundred bucks to drain the engine before any damage ocurred- which could have been covered by insurance. "Americans make this mistake all the time"> even without the fuel screwup, there are serious wind storms that can tear a door off your car (not trying to scare you, but the environment can be tough)

I liked the food a lot even though it is not their forte.

I loved the fish stew (similiar to fish chowder) arctic char and salmon. They also specialize in lamb dishes, and hot dogs are a big deal. Like anywhere else, if that doesn't float your boat you can find stuff like pizza.

Le Cock - is a great burger joint in Reykjavík owned by an American with a sense of humor.
The Lebowski Bar in Reykjavík is a must- the entire bar is designed as a bowling alley with dozens of different White Russians on the menu (our one booze recommendation) This is not just my opinion, man.
Don't plan on going in the ocean- besides being freezing cold, its very treacherous.
The beaches are all black sand!
Lots of amazing natural beauty.

Have fun!

There is more hiking and camping available as mentioned below, but a little less opportunity for the ice caves. Snorkeling the Great Divide (as mentioned below) would be awesome if you go in the summer - I would google it and watch a video on this if its something you are considering.If you do go in the summer your lead time to book stuff increases

dream. Lots of great trails, waterfalls, glaciers to hike around. For specific info you will have to be more exact in who is going and when. There are certain parts of Iceland that basically aren't available to go to in the winter months.

You can certainly do the Blue Lagoon (it is definitely most famous) but there are some other good ones around Reykjavík. Agree that there isn't much to do in Reykjavík - maybe spend a 1/2 day there at most. If you have young kids there is a volcano show in Reykjavík that was pretty cool.

The Golden Circle is a good option over the Ring Road if you are going in non-summer months.

Last thing, don't think you will save money. Iceland rivals the other Nordic countries in costs. It is sort of like Hawaii but there are no palm trees.

Get in the car and drive the golden triangle. Go during the summer and enjoy endless light.

Find the mountain and get him to press you over your head

Workout with Annie thorsdottir at CrossFit Reykjavik.

Blue lagoon

Walking food tour of Reykjavik

We did a few glacier hikes. Seeing one calve off something like 50 tons of ice was wild.

Bobby Fischer is buried in a nondescript churchyard in a small town by Selfoss. It isn’t otherwise worth a visit but it’s an easy drive as part of a longer road trip.

It’s not that it’s a bad city, but it’s just a city, nothing special. The rest of the country has alien-like beauty that’s hard to describe. That’s where you should go.

I’m busy right now so I can’t get too in depth, but if I had one piece of advice, that would be it.

Forest Lagoon is an awesome geothermal spa. They also have an outdoor geothermal swimming pool with waterslides and such (open year round). Plus, you can catch a ferry up to Grimsey, the only part of Iceland that lies within the Arctic Circle (three hours each way, and it can be a rough ride, but it'll allow you to say you've been inside the Arctic Circle). Akuyeri is a 5-hour drive from Reykjavik, though, so it's a commitment.

You could drive south and check out the black sand beach at Vik. There are a variety of other outdoor sights in the area as well. Vik is about three hours from Reykjavik.

I was lucky enough to live in Iceland for a year, so I got a chance to explore the whole island. I get that these ideas might not make sense of you're only spending 4-5 days in country.

Sadly, I was ghosted. But that looks like a cool place to spend a few years.

They allow whaling. My peeps!!!