Just done a long weekend there!
Fantastic place. We did most of the standard touristy things as it was relatively easy: Northern lights, Golden Circle, South Shore, Blue lagoon. I’d say you don’t need to do blue lagoon (its very expensive for a warm bath) but the others were really good. Lots of very pretty places and even just driving throug the landscape is pretty mesmerising.
You won’t need more than a day (afternoon really) to look round Reykjavik itself. Nothing wrong with it, just not much there.
Icelanders really like hotdogs so there’s a few cheap and cheerful and some “gourmet” places around. If you do any day trips probably best to take at least a snack as there’s not many opportunities to eat (cheaply) out in the “wilderness”. The classic stock up during buffet breakfast is well recommended.