I’ve been there about six times now both alone and with groups, in winter and summer , staying in hotels(look up hotel Budir on Snaefelsness peninsula) , camping (north west fjords) and in huts (landmannalaugar area) Imo you can go anywhere outside Reykjavik and it’s beautiful. Most start with seeing all the hotspots in the Golden Circle but imo you don’t need to, really. There is a ringroad around the whole island that many drive around. The light in iceland combined with the sometimes mordor like landscape is very beautiful. But , the weather can be totally crap as well.