Love going on my own. This year will be going to Botswana and hopefully doing New York Marathon again. Have gone to Kenya, Costa Rica, Hungary, Argentina, Uruguay, Namibia, South Africa, Egypt and various other countries as an independent female traveller, and never experienced any problems. If I want to have time alone, it's great, and if I feel the need to go and chat to someone, I do the typical English tourist abroad bit and wear a football shirt, never fails to spark a conversation (had a very interesting conversation with a local guide in the middle of Mongolia about England's inability to take penalties).
Have a great time.