Three days is enough to get a real feel for Tokyo without rushing from one checklist spot to the next. This plan is built for traveling alone: easy mornings, areas that are close together, places where eating solo is normal, and a couple of chances to talk to someone who lives here. Swap days around to suit the weather.
Buy Me a Matcha is a free, friends-only iPhone app for meeting one new person over a matcha or coffee, all in English. No dating, and you can choose to meet only women.

Three days is enough to see a good mix of old Tokyo, the big-city side and a couple of relaxed neighborhoods, as long as you keep each day to two or three areas.
Yes. It's safe, public transport is simple, and eating alone is completely normal at ramen counters, sushi bars and cafés.
Hostels with common rooms, small group activities, language exchange nights, and friends-only apps like Buy Me a Matcha, where you can meet someone who lives in Tokyo over a matcha or coffee in English.
Anywhere close to the JR Yamanote line, such as Shinjuku, Shibuya, Ueno or Tokyo Station, keeps travel times short.