We went to Iceland with our campervan, by ferry in the 80s. What I remember as being worthwhile were Strokkur and Geysir, and Goðafoss, all within a day trip from Reykjavík. Bound to be busy, but worth seeing. I seem to remember an arboretum or something of the sort in Akureyri. There's also Glaumbaer farm museum which might be reachable from Akureyri or Árbaer near Reykjavík. Any of the waterfalls are worth seeing and Reykjavík itself warrants a good wander round. I envy you! Have fun.
I didn’t go on a cruise but stayed in Reykjavik for a few days. We went on trips from there. The trips were full days and we seemed to cover lots of miles. I’m not sure if we would have been able to see what we did unless we had hired a car. Try googling Reykjavik excursions and see what they charge. Ships tours are expensive but then so is Iceland.
We are going on a P&O cruise soon that visits Iceland. We like to do our own thing because the shore excursions are so expensive ( we recognise the pitfalls of this) yet don't want to miss anything really spectacular. Does anyone have any advice ? We are calling at Reykjavik , Akureyri and Isafjordur