Onsen is one of my favorite, so whenever I had the opportunities I would spend an hour soaking in onsen. There is a couple of sento or bath houses in downtown Tokyo that are wonderful.
To visit sento, you also need to get armed with an open mind and some Japanese yen. Optionally you should bring a small towel for scrubbing/drying off, a quality body lotion and soap, with a bottle of water to keep you dehydrated. However, all the optional items can be bought or rented at inexpensive price. Sometimes a public bath chooses a day in a week to be closed for regular cleaning and maintenance, so it is good to check which day it is, commonly Monday/Tuesday/Wednesday. Public bath normally operates from 3pm onwards through midnight, but some public bath is open a shorter during in AM for a morning soak.
A sento commonly provides small and medium towel rentals, as well as soap and shampoos/conditioner either complimentary or at sale. Normally there is also a laundry shop next to it.
You approach sento, remove your shoes in one of the shoes locker, keep the key, and purchase a ticket on vending machine. Then, hand your ticket to the cashier to obtain entry.
The cashier is located at a lobby or bathing entrance area that generally also has multiple items available for purchase such as travel size soap, shampoo, conditioner, souvenir towel. It will have a drink vending machine that has mineral water and milk.
Notice the entrance to women and men changing area, and do watch out to enter the right area! There is often a smaller red and blue banner over the entrance of each area respectively.
At the changing area, remove all article of clothing and store them in the lockers provided. The lockers would use coins that is either refundable or costing 100yen per use. There is also a toilet which you can use to relieve yourself prior to entering the bathing area. Slippers are always provided for you to wear while using the toilet.
With a small towel and bottle of water, enter the bathing area and start washing yourself. The courtesy is to cleanse yourself and shower as well as cleanup the area afterwards without hogging a seat. From health standpoint, showing with super hot water allow you to acclimatize your body to the heat of onsen water at the start of your bathing experience.
Once you are clean, you can choose the first pool to soak in. Enter the pool carefully, holding the railing if needed to test the heat of water. I generally keep my towel folded on my head or safe on the shelf. It is considered rude to soak your towel, and long hair in onsen water, so do tie or bun up your hair before entering a pool.
Some of the recommended bathing houses in Tokyo:
Daikoku-yu 大黒湯 nearby Skytree: This public bath house is one of my favorites in Tokyo. The name literally means 'big black bath'. It is a really nice onsen especially with an outdoor area that has divine pools and a chillout area on deck where there is swings. Note that this outdoor area which every day and is on the men's side on odd days, and women on even days. One of the two outdoor pools is a large pool with milky bath that has a spacious soaking area and a sitting spot. The other outdoor pool is a refreshing cool plunge bath where you can see the top of Skytree on a clear sky. The smell of the oak/pine? pillar that is being heated from the onsen water gently wafted through the air, is so relaxing to your sense of smell and well-being. Then you can return to indoor area where there are four pools: a soaking bubble pool kept at 35 degrees thus popular for long soak and for children, a seasonal herbal pool with different water every day (when I was there on July 8th, it was rose), massage pool with super jet (at super hot 42 degrees water), and a small cooling pool. Soap and shampoo/conditioner is provided for free with no charge for hair dryer. Closed on Tuesday.
