One of the most convenient ways to travel in Japan is using an IC card, pre-paid cards that you can load up and use as a debit card for travelling. They allow you to quickly scan and pass gates to the subways or pay for bus fares. In addition to that, you can use them to quickly pay at convenience stores. The con of this is that it is simply too convenient that you can easily pay quite a bit if you are not paying attention. Of course, transportation in Japan is cheap since they are usually 200-500 yen (~2-5 USD) for one way, but if you plan to practically explore a whole city like me, that amount can exceed $100 USD. If you plan on only going to a few places by the subway, then IC cards are the way to go!
Tokyo Subway Passes
The Tokyo subway passes allow you to take subways from the Tokyo Metro and Toei Subway lines for an unlimited amount of times for as long as the time indicated on the ticket you buy and only in Tokyo. You can buy passes for 24, 48, or 72 hours. For adults, the passes will be 800, 1200, and 1500 (or $8, $12, and $15). If you know where you want to go and will be using the subway a lot, this option will sound very attractive to you. The con of this is that it does not include the JR lines, so if you were planning to use those, you might want to rethink about buying these passes or planning a new route to get there.
These passes are only sold to foreigners at airports, some designated hotels, and designated vendors, which you can find here:
You will need your passport to buy one, so keep it handy when you arrive.
One of the most important things you need to do before deciding on which option you want, is to calculate how much you will spend on transportation per day. Then, group the days together according to their prices. Try to place the three most expensive days in consecutive order and if their price exceeds 1500 yen, I definitely recommend thinking about getting a 72-hour subway pass for those three days. For example, if you are visiting Harajuku, Shibuya, and Akihabara and the cost to visit them in the first three days is 2000 yen, it would make more sense to buy a 72-hour pass for 1500 yen instead because you still get to go to all three places at a cheaper price. ~5 USD may not seem like a lot, but any amount of money saved would be helpful, right? I'm still unsure if you're allowed to buy more than one 72-hour pass at the same time, but if you can, then it'll definitely help you save more if your groupings of the days always exceed 1500 yen.
The next thing to check if you are thinking of getting a Tokyo Subway pass is looking at a map of all the places the subways can take you to make sure your destinations are included.
Highlight the places you want to go to make sure the Tokyo subway will allow you to reach that area. It'd be a waste of money if you wanted to go somewhere and buy the cheaper option just to realize the option won't take you there.
My advice for saving money on transportation is prioritizing the Tokyo Subway passes and asking travel agents if it's allowed to buy more than one of their passes at a time and add about $10 onto an IC card since you can always add more to the IC cards if necessary.