Welcome, and yes it is disgustingly humid here in summer.
It depends how you want to kill your time and also how much longer you have in the city. Ginza is known for higher end, shopping, eating and drinking. You could stroll down to the Imperial Palace and have a wander around there (note: there is not a great deal to see as you can’t go into the palace, but the grounds are nice and has a nice view of the skyline of Marunouchi / Otemachi).
You could jump on a train and check out one of Shibuya, Shinjuku, Yoyogi, Harajuku, Omotesando, etc (all in the west). Two of my favourite ways to kill time is to let off some steam in the batting cages in Kabukicho (Shinjuku) and wander around Shinjuku Gyoen (Tokyo’s botantical gardens). Yoyogi Park is great for people watching - and you can visit the Meiji shrine while there - but I would perhaps save that for the weekend when at its best.
You are also relatively close to Asukusa, home to the Asakusa Shrine (the most famous in Tokyo) - just head north on a train. You can check out the Skytree and Ueno Park while up there. I would probably save this though for when you have a bit more energy - it is the most (and perhaps one of the only) touristy parts of the city and can get pretty full on / busy. Saving it for Monday if you are still here would be ideal. Kappabashi - the home of cooking supplies (in particular, plastic/wax food) is worth a stroll and a laugh in that area also.
It goes without saying that you are close to Tsukiji fish market and you should check that out one morning.
Also recommend checking out a baseball game while here. The Tokyo Swallows play in a small stadium in the middle of the city and the atmosphere is great on a summer night.