Last updated : May 12, 2017
Unfortunately the image that Tokyo is an expensive city to travel is true to some point.
There are also no tourist tickets that combine unlimited travel on local trains and free entry to attractions that can be found in many major cities.
The below is the few options that are available with my personal opinion as reference.
Tokyo has two companies operating the subway system and first-timers will probably have difficulty knowing which lines belong to which.
1) Tokyo Subway Ticket (http://www.tokyometro.jp/en/ticket/value/travel/index.html) is what I consider a real bargain - especially the 2 and 3 day versions - as it allows unlimited travel on ALL of the subways running in the Tokyo area.
The one day version is 800 yen, while two days is 1,200 yen and three days is 1,500 yen.
Starting March 2016, the tickets are now good for 24 hours (or 48/72 hours) after the first usage, making it an even better deal!
There are also versions that combine travel from the airport with this ticket.
The Narita (Keisei Skyliner) version
The Haneda (Keikyu) version
Airport Limousine version
All of these passes must be purchased at the airport by showing a foreign passport. Also this does not allow rides onto the JR Lines or any of the other private lines that operate towards the suburbs.
2) Tokyo Metro 24 Hour Ticket (http://www.tokyometro.jp/en/ticket/value/1day/index.html) is available for 600 yen and allows unlimited rides on the nine lines run by the Tokyo Metro company. In other words, there is no entry to the Toei Lines such as the Oedo Line or Asakusa Line. With careful planning, you should be able to visit most of Tokyo's top attractions. (One exception is the Tokyo Tower; the Oedo and Mita Lines have stations nearby, but they belong to the Toei Network so you cannot use this Metro ticket) Beginning on March 2016, the tickets are now good for a full 24 hours after you first use it - making it far more convenient for users who want to start using them from the evening.
3) Toei One-Day Economy Pass (http://www.kotsu.metro.tokyo.jp/eng/tickets/value.html) is the one-day ticket on offer by the Tokyo Bureau of Transportation, which is the operator of four subway lines for sale at 700 yen. The pass also allows rides on the buses as well. With less options on the subway, you'll really need to do the homework before deciding if this the right ticket for you. Unlike the Tokyo Metro ticket, the Toei pass is only good until the last train of the day.
4) There is also a pass that combines both the Tokyo Metro and Toei 1 day pass available not only to visitors but also to local residents at 900 yen but obviously it will make more sense to buy the Tokyo Subway Ticket in option 1.
5) Finally, if you don't want to pre-determine whether your ticket will work or not, the Tokyo Free Kippu (http://www.jreast.co.jp/e/pass/tokyo_free.html) will allow access to all JR lines, subways and Toei buses. But at the price of 1,590 yen, you'll need to do a considerable number of rides before you can get good value from it. (One subway ride is about 170-210yen)
By buying the above passes, it will put a restriction on your itinerary, especially if you want to decide on the spot where you want to go next.
It may simply be wise to buy IC Cards such as the Pasmo (sold by the subway and private train operators) or Suica (sold by JR). It works the same as the Oyster Card in London or the Octopus Card in Hong Kong; you just tap the card against the blue screen when you get in and out of the station and the fare will be automatically deducted from the card. You can top-up whenever the card runs out of value from the ticket machines at the stations. Not only do these cards work on almost all trains/buses in Tokyo, these cards are accepted on increasing number of train systems outside of the city as well, such as the subways in Sapporo, Sendai, Nagoya, Osaka, Kyoto and Fukuoka.
Note: The discount you receive when using Pasmo or SUICA is only about 10 yen per ride at the most; these cards are mainly for convenience rather then saving money. Nonetheless, this is the favoured format of travel for many of the locals.
If you plan on doing some museum visits, the Grutto Pass is a booklet that will allow free or discounted entrance to over 70 facilities in Tokyo including the Edo-Tokyo Museum, Miraikan, the Ueno Zoo and Kasai-Rinkai Aquarium. The ticket is ideal for residents like me as they are valid for two months after the first use, but visitors here only for a few days could still get some value out of it depending on the itinerary. Check the website to see if any locations on your plan is participating in this program.
The pass can be purchased at the ticket office of any of the participating facilities.