Visit to Tokyo

[3sixty]

I have booked flights for a short trip to Japan (5 days) and will be flying by ANA from Kuala Lumpur to Tokyo

I've never been before but since we live on this side of the world now we are slowly exploring the rest of Asia. I'm after a few pointers:

• We'll be staying quite central in Tokyo and assume the metro/underground is the best way to get around. Can I buy a 5/7 day unlimited use pass? Or is it better to buy individual trips?
• We are also planning an overnight stay at Mount Fuji. Is it better to book the bullet train in advance? If so, where is the best/cheapest to buy?
• Any recommendations of some good places to eat? We will be staying around Nishikasai
• Anything else we should be aware of / must visit / need to know?