Hello,
My tip is to get out of Reykjavík and rent a car and drive around or fly. See some volcanos or glaciers that’s always good a bit of hiking is required for most but worth it, Snæfellsjökull is a nice one to visit. And always a favourite of mine as it’s close to where my some of my family is in Akureyri is Jarðböðin við Mývatn (Mývatn Hot springs) it’s great, it’s about 80km east of Akureyri. Good chance if your in that area you might see the northern lights too but I think it get harder to see heading into May.