None of the subways are included in the Japan Rail Pass. The only lines that you are likely to use in Tokyo that are included in the JR Pass are the Yamanote, Chuo, and Sobu Lines, and possibly the Joban Line, all of which are above-ground commuter trains.

The Yamanote is a lumpy circle around the central city. The Chuo Line bisects the circle at Tokyo and Shinjuku and runs to the western suburbs. The Sobu partly follows the Chuo but stops at more stations and veers off to the east at Iidabashi.

You can also use the JR Pass to take day trips to Kamakura and Nikko and for the Narita Express.

If the station doesn't have JR in its name, you can't use the pass on the trains that run through it.

The JR Pass is mostly useless within Kyoto, unless you go to the cheesy Uzumasa Movie Studio, although you can use it to take day trips to Nara, Fushimi, Osaka, or Kobe.

It is mostly for intercity travel, and for that purpose, it is a bargain available only to tourists that makes Japanese people and long-term expats sigh with envy.

For travel within cities, get a local Suica or Pasmo debit card (for Tokyo) or a bus pass (sold in 24-hour segments) for Kyoto. With a Suica or Pasmo, you can transfer between JR and non-JR lines with the fare automatically deducted from your card, and if your card zeros out, you can add more money at any train or subway station, as with London's Oyster Card.