Maybe I'm late to the party, but here's my opinion (as a male):
Japan is completely safe, and I feel that the Japanese think so to. During my stays for study and holiday I have seen many women walking by themselves at night. Even small children can be seen travelling all by themselves. Japanese people are very friendly and very helpful. Many years ago, on my first day ever in Japan, I got lost and a friendly woman drove me around to look for the hostel together. Incredible! At a different point I once got lost, asked for directions in the police booth, and got a ride in a cop car to my student dorm
Concerning cost for travel: this depends heavily on what kind of person you are. In my opinion the most awesome thing in Japan is free: walking the streets of bustling area's, observing people in their daily routine, etc. Other people like to visit museums and things like that. I believe you can get a Tokyo subway pass for about 1000 yen per day, a domestic flight with Peach for about 3000 ~ 8000 yen, a bus ride from Tokyo to Osaka for 3000 - 5000 yen, etc so transport does not have to be expensive.
Food is good and available in so many places. Casual dining places, mom and pop restaurants and decent chain restaurants will serve you typical Japanese dishes for 500 - 800 yen.
What you spend on ho(s)tels is completely up to you. I would not be too stingy though, as sleeping in a shady place with poor management will really affect your mood and experience. I would pay 2000 - 3500 yen for a hostel, or around 7000 for a hotel. Chains like Chisun Inn are cheap yet decent.
I could definitely visit Japan in two weeks on 2000 Euro including the flight ticket, and do everything I want. Again, this depends on the person