Don’t think the taxi rate is absurdly high, but the distances between different places in Tokyo can be vast. If you taking a taxi, beware that they may not be able to read English letters, or even a map. If you can find a Japanese address to the place you’re going to it’s much easier. We prepared by pre-opening a wiki-site for the place with the hotel wifi, and zooming in on the Japanese name to show the driver 
However this was in Kyoto, things might be different in Tokyo.
Subway is actually very good. You can get a PASMO card which is a prepayed card that works on all subway and commuter trains. You can get it in a machine at the station (English available). I prepayed 5000 yen that was enough for 2 weeks. And if you have a lot left when you leave you can return it and have most of the cash back. There were quite a few subway map apps, don’t remember the best one. Just try them all
The Tokyo Tripadvisor app is pretty good as well.
Ghibli museum I think you have to book in advance, we didn’t go.