@Bronwyn depends on what you want to do. There are tons of tours if you want to see the usual sites.
You might try asking a travel agent. They actually don't cost anything to consumers, bc most prices in the tourism industry have a travel agent markup, whether or not they're sold through an agent.
But if you want to set your own itinerary and see remote stuff, renting a car is probably the play.
When my wife and I went in 2016, we concluded that we should have just eaten groceries, as the mid market restaurants are not very good and are super expensive. If you treat it like a super frugal trip, Iceland doesn't have to break the bank.
@acjay thank you! I love solo travel but I usually do it in the US or Mexico so this would be a new adventure but I just happen to have time in mid-august...