You'll probably have a good time at the theme parks by yourself... I mean, think about it, you can go on whatever rides you want however many times you want, you can take breaks whenever you want, and you don't have to argue over where you want to eat. My only piece of advice is DO NOT walk around Orlando or any of it's suburbs alone, especially at night. Orlando has a lot of violent crime, and a woman walking around by herself would be an easy target. Maybe drive over to Tampa/Sarasota area and go spend the day at the beach. If you want to go shopping at all Mall at Millenia is in Orlando and it's a pretty awesome place, they also have some good restaurants in there. Have fun, just make sure to stay safe.
Edit: Obviously the people who are saying Orlando is a "family friendly" place and that the tourist areas are "very safe" do not live in or around Orlando. I've lived 30 minutes from Orlando my entire life. Yes the theme parks are safe, but I wouldn't say outside of them are.