If you want to travel around Tokyo (or anywhere in Japan) smoothly, I would suggest that you get your own pocket wifi first. And always bring along with you your mobile phone! :)
Whenever my friends or readers ask me about an APP / website about the train information, I would always suggest “Hyperdia”.
You have to access it by typing the whole “www.hyperdia.com” url. It is available in three languages: Japanese, English & Chinese.
“HyperDia” is a service which offers the route and the timetable of the railway and the aviation of Japan. With simple operation, “HyperDia” guides the optimal route and the fare from starting point to end. The route search engine is made by self-developed technology. By applying this route search engine, it is possible to make link to regional information, for example, map information, a rental car and the golf-course etc around the station from the search result. So, it is possible to offer the information which is possessed with your corporation sight effectively. (from their website)