Safety in Tokyo
Tokyo is probably one of the safest big cities you will ever visit, and Japan in general is one of the safest places to visit in the world. Most people, including single female travellers, would not encounter any problems walking along the streets alone at night. Street crime is extremely rare, even late at night, and continues to decrease. However, "little crime" does not mean "no crime", and common sense should still be applied as anywhere in the world. Often the biggest risk is travellers taking Japan's visibly apparent lack of crime too close to heart and doing things they would never do back home.
The most common crime is sexual harassment on crowded trains, pressed up against each other, hands wander. This is more of a local problem as westerners are considered more aggressive and would stick up for themselves. The best way to deal with any wandering hands is to yell "Chikan!" which is the Japanese term for "pervert"
Small police stations, or kōban (交番), can be found every few blocks. If you get lost or need assistance, by all means go to them; it's their job to help you! They have great maps of the surrounding area, and are happy to give directions. They may, however, have difficulties with English, so some knowledge of the Japanese language helps.
Take the usual precautions against pickpockets in crowded areas and trains. Also be aware that theft is more likely to occur in hangouts and bars popular with travellers and non-residents.
The red-light and nightlife districts can be a bit seedy, but are rarely dangerous. Note some small, back-street drinking establishments in red-light districts have been known to charge extortionate prices. Similar problems exist in the seedier upscale clubs in Roppongi, where it may be wise to check cover charges and drink prices in advance.