Major downtown such as Shinjuku, Shibuya, Ginza are safe enough for a female solo traveler. (But avoid staying in Kabukicho area)
There are many guest houses which have female only dormitories. Hostels such as Nui. in Kuramae is beautiful and stylish. Staying in a ryokan (Japanese traditional style of accommodation) will be a great experience, too.
These articles may help you: