The only thing you need to do in Japan is bring their manners with you.
Okay, the tips are not in order, I’ll just write what ces to mind =p
For one week, it is recommended you buy a train travel card. I spent about $150 on 2 weeks on trains since my goal was to live like a non-tourist xD
1 week of mobile data shouldnt cost much.
If you intend to stay in Tokyo only and want to be adventurous, simply walk around and get lost. Use your phones gps when you need to find your way.
If you are backpacking and arnt intending to buy anything major over from Japan, you can cut cost with low cost airlines. The travel experience probably sucks but save where you can xD
Eat convenience store food.
If its only 1 stop away inside central tokyo, walk.
To be honest, you only need to plan if you intend to visit tourist attractions. I am one of those who rather venture unrestricted to plans but I understand some people must have a plan.
You can try to plan areas pack with attractions to maximise time.
Example: Asakusa station has a really large shrine and tokyo sky tree just 30mins walk away. Theres a nice river and shoping district along your walk so its not gonna be a boring walk.
Meiji shrine is near harajuku where the fashion street is (about 40mins stroll) the shrine closes at 6pm but thats about the time harajuku fashion street opens. Near the street is another shrine hidden, explore a little to find it.
I’ll tell you, the yamanote line (green) itself has so much attractions. Just walk station to station, theres so much to see.
Just bring money, a phone and yourself. It will be a great adventure. In my phone was a translator and maps, thats how I communicated on my own xD
Have fun!! Just thinking about it makes me so excited. Brings back good memories =p
Ps. I know you mentioned not to talk about toilets but its really hightech!