Blue Lagoon, Perlan (good museum downstairs, 360 degree view of Reykjavik on the observation deck, great ice cream….but expensive food…), The Golden Circle (Gullfoss, Geysir, Skogafoss—and you’ve got to climb Skogafoss…jump up and down and feel how hollow it is up there!!!!) and Thingvellir for Icelandic history and the Mid-atlantic ridge (where the North American and European tetonic plates are slowly separating)
The pic is the view from the top of Skogafoss.