How much does it cost to enter and leave the same station (JR line, Tokyo)

It should go without saying, but since some people seem unclear on the concept, I state explicitly that riding a train without paying the correct fare is not just "dodgy" or any other euphemism you can think of, but a violation of the Article 29 of the Railway Act (not to be confused with the Railway Business Act) and also constitutes fraud under Article 246 of the Penal Code.

That being established, what is the correct fare when you enter and leave from the same station? It depends on the actual departure/arrival station and route you take, so it is impossible to answer the question without knowing them (but it can certainly not legally be done with just an entrance ticket)

Now, the general principle is that the fare is to cover the costs of you riding the train, not of you passing through the ticket gates, and so whenever you ride a train, you must pay the corresponding fare, regardless of whether you exit the gates. Note for example that "station entrance tickets" very explicitly state that you may not ride a train*.

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The fare is calculated based on the route actually traveled by the customer, as well as the order of departure and arrival. (link)

However, the usual exceptions apply, including the one that says that if your route is contained entirely within one of five "large city" zones, then regardless of the route written on your ticket, you can use any other route that you want between the same departure and arrival points. In practice, this means that you can buy a ticket for the cheapest possible route, and actually use any other one that you want.

Example 1: suppose I want to make one round of the Yamanote line starting and ending at Tokyo station. A possible route from Tokyo to Tokyo is via Kinshicho and Akihabara, so I can buy** a Tokyo-Kinshicho-Akihabara-Tokyo ticket and make my Yamanote circle trip, no problem.

This is further complicated by the fact that not every route is a route, so to speak. In particular, for ticketing purposes a route may not contain any loops or duplicated sections, and in your case you may well have at least one of those, since you want to go to some particular station and back.

Example 2 (loop): Suppose I want to do Kinshicho-Ochanomizu-Kanda-Ueno. Because this has a loop (Akihabara-Ochanomizu-Kanda-Akihabara), the correct fare for this trip is Kinshicho-Akihabara plus Akihabara-Ueno and not just Kinshicho-Ueno. In general, when you complete a loop, your trip is automatically "cut" into two separate trips at the last station of the loop.

Example 3 (duplicate section): Suppose I want to go from Tokyo to Atami and back. Because this will require duplicating the section between Atami and Chigasaki, I must pay both Tokyo-Atami and Atami-Tokyo. In general, when you "backtrack" at a station, your trip is automatically "cut" into two separate trips at that station.

Example 4: However, I can go from Tokyo to Chigasaki and back with my Tokyo-Kinshicho-Akihabara-Tokyo ticket, because it can be done without any loop or duplicate section: I can go from Tokyo to Chigasaki via Shinagawa and Yokohama, and then back via Hachioji, Shinjuku, and Akihabara.

Note that all those examples are if you do not exit the ticket gates, as per OP. As I have mentioned elsewhere, tickets for travel within the five large city zones do not allow exiting the ticket gates before your arrival point (stopovers).

* Now, like many other things that are in principle not allowed, you may or may not be able to talk an agent into letting you get away with it, possibly by feigning ignorance (especially if you are a foreigner). Personally, I find this practice abhorrent.

** A ticket with the same departure and arrival points can be purchased at ticket offices only. Not at ticket machines, online, or via an IC card.

First up, this is a bit dodgy and I'd suggest perhaps just paying the fare...

As for the technicalities - you won't be able to tap out with Suica at the same station on JR, you'd need to go to the attendant and ask them to do it manually. If it's 2 hours after you tapped in, they may ask questions.

You can buy paper 'platform tickets' to see off people at some stations without traveling, and as there aren't conductors on trains you could get away with this also.

A platform ticket is called a ??? (nyuujooken), it allows you to enter the platform area to see people off.

Suica unfortunately cannot be used as a platform ticket. If you try to tap out at the same station, it won't let you.

Platform tickets can be bought at the paper ticket vending machines -- and you can use your Suica to buy paper tickets. They are ¥140 for most of Japan (see https://www.jreast.co.jp/kippu/18.html).

First of all, this is not dodgy.

It is legally fine to ride a train without paying anywhere you want unless you exit the station or ride in reserved cars.

All you need is to visit the guy in the window near the gates when exiting and explain that you did not exit the station on the other end. They will remove the ??? price (about 140 yen) from your Suica/Pasmo and that's it. You do nothing illegal, so even if they ask why did it take 2 hours, you could kindly explain.