Read the many recommendations and blog posts on I Heart Reykjavik. I got lots of great info there including restaurant recommendations.
Get a cinnamon roll at Braud and Co. They have lots of other pastries too. Try those if you want but don't miss the cinnamon roll.
See the three highlights on the Golden Circle: Gullfoss, Geysir and Thingvellir. Decide whether you're going to rent a car and drive it yourself or take a tour. Pros and cons for both. We drove ourselves. Here we are overlooking Gullfoss.
If you drive yourself, plan to have lunch at Fridheimar Tomato Farm. This was super unique, delicious and fun. If you decide to take a tour consider one that has a stop here.
If you want an additional stop on your Golden Circle tour, Kerid Crater is really cool.
Splurge and go to the Blue Lagoon. Everyone seems to love it. We did this last time we were in Iceland (17 years ago) and the price has risen dramatically.
Or get the geo-thermal spa and water experience at Fontana instead. (Or another pool or spa, there's several.) That's what we did. It was cheaper, already on the way to something else we were going to see and less crowded than the Blue Lagoon. But there is no silica mud mask. I'd say both are in stunning locations. Blue Lagoon in the middle of a lava field and Fontana on the shore of a lake. See the lake behind us here? You could soak in the naturally-heated pools, then walk right out into the naturally-COLD lake. (I didn't, but Jeff and Claire did.)
Walk along the shore from Harpa to Sun Voyager.
We didn't have time for many museum stops, but Tales from Iceland was pretty fun. It exceeded our expectations.
We really enjoyed the live theater production of Icelandic Sagas.
Walk around the old harbor area near the Maritime Museum -- I believe the area is called Grandi. It's trendy and nice. We ate at Lamb, Flatey and Valdi's. I wish we could have taken the tour at Omnom chocolate.
Obviously, there's lots more to do. Of the things we enjoyed, these were the highlights. Let me know if you use any of our tips.