Iceland is the perfect country for solo traveling. The crime rates are very low and it is very safe for women to travel here solo as well. I've done it for seven years now and I've never had any bad experience.
If you rent a car and just drive around, you will have the time of your life! If you are planning to go to Iceland alone, but you don't want to drive everywhere by yourself, you can check out this website: www.samferda.is There you can find other people that are searching for a ride or that are offering rides. It is very common in Iceland to share rides, so if you feel like meeting new people, this might be a good plan!
This itinerary is not how a normal itinerary looks. I haven't made plans for you per day, but on day one I've combined all the accommodations that are best for solo travel. There's a lot of accommodations in Iceland, so I thought it would be easiest to have a list of the ones that are great for solo travel. Especially if you are on a budget, these are good to check out.
Day 2 has several of my favorite tours, that are also perfect if you are traveling solo.