What clothing to wear?

This may seem like an absurd question but I will be living in Japan this summer for three months (June through August) and have been trying to decide what clothing to bring along. For my civilian-military job I have a uniform so that part is taken care of, but what I am really worried about is what clothing I should bring for my weekend travels.

After a bit of research I am completely baffled. Several sites have me worried. As an American (barely 20 so I am a bit scandalous in what I can get away with) I think nothing of wearing my skimpy summer clothing, but what should I wear in Japan in summer? I am somewhat bigger in the chest region than most people my size so they naturally stick out. My real question is: will I be offending anyone if I run around in a tank top and shorts? And will cleavage be a big no-no?

Japanese people tend to cover up more than Americans for example do, generally speaking, although short shorts were fashionable among some women the last couple of years. It's very rare to see cleavage here- expect a lot of looks if you do wear a low top and you are well endowed.

Most people don't wear shorts in central Tokyo, although a lot of younger women wear sleeveless tops.

Also, although it is very hot outside in summer, the A/C in trains and buildings can be quite strong, so you will get chilled very quickly once you go inside. This is made worse by the humidity causing you to sweat a lot- you freeze as soon as you go somewhere airconditioned.

I wear tanktops, but always carry something light to put on over it when I get on a train or go inside a shop or restaurant.

Yes-
definitely two
separate individual
NOs..

There is a strange double-standard in Japan...

Showing your arms below the elbows seems to be scandalous and cleavage is "eroi", but wearing shorts or skirts that show your panties with the slightest breeze or give you cameltoe is fashionable.

I get a lot of strange looks for tank tops. No one else wears them on the street (here they are sold primarily as underwear).

I would say it is showing your shoulders that a lot of Japanese people avoid, showing your forearms is quite common, but in Tokyo at least it isn't really that rare to see younger women in tank tops either in summer. Possibly different out in the very rural areas.