Some things you should know/have:
Cash: Tokyo is a modern city but there are still a ton restaurants and stores that only take cash. Most people carry large amounts of cash on them regularly and the city is a pretty safe place, so you don’t really have to worry.
Suica/Pasmo: Trains and subways are the preferred mode of transportation. Nobody wants to worry about constantly buying and keeping track of tickets.
Bag: Everyone’s got one. Purse, messenger bag, backpack, etc. I’ve seen a lot of guys with Coach, LV, Prada, and other brands, carrying bags that look like purses. I’m not sure what’s going on there…
Towel: Summer is hot and you will sweat if you go outside. Everyone carries a small towel or handkerchief with them, to wipe the sweat from their brow.
Map/directions: Navigating the Tokyo can be pretty complex if you’re looking for a specific location. Usually only a few major streets will be named in each area/ward/neighborhood. Everyone gives directions with station exits and local landmarks. Most areas have specific landmarks that everyone knows and refers to. Try to learn them all.
Headphones/music: Sometimes it’s nice to have a soundtrack to your life.