Welcome to Tokyo!
Nakano Broadway - the watch place in Tokyo
The place for watch browsing is Nakano Broadway. It's a very old school mall with probably 10-20 watch sellers (used/gray). Get out the Nakano subway station in the North direction, and you will see the entrance just on the other side of the square.
As you walk along the corridor, you will see some smaller vendors. Some of them have some affordable watches (Kitamura Camera, TWC).
As you keep walking straight, you will get after a while to the real Nakano Broadway (there's a sign). As you enter, take the escalator or the stairs to the right to get to the second floor where the biggest retailers are located. They are clearly not focusing on affordable watches, but they have an incredible selection. The biggest and busiest are JackRoad, Watchnian and Kamekichi; but there are many more. And if you find the one that sells only Speedmasters, please tell me where it is! I have been there a dozen of times, and never found it, it's a maze.
Other places
Every shopping district in Tokyo has tons of watch shops, independents or ADs.
Some of my favourites (all super-high level stuff)
Ginza
Rasin (there are 2 or 3, one of which dedicated only to Rolexes)
Shinjuku
the 4th floor of the Isetan mall is full of big brands ADs
watchnian (although much smaller than the branch in Nakano)
GMT (south-west of the station)
Shibuya
House of Kiroba
HMS (small shops, specialize in microbrands)
Affordable
Don Quijote - that's the quintessential chaotic shopping center in Japan. They are everywhere, and watches tend to be for some reason at the upper floors or at the floor immediately below it. Almost everywhere, they will have Seiko, Citizen and Casio. In very few places (Roppongi branch for example) they have Omega, Tag Heur and Longines.
BicCamera and Yamada as other have said. As usual Seiko, Citizen and Casio. Pure chaos, sometimes difficult to find where the watches are.
Books off/Hard off. People suggest them, but honestly they are more a miss than a hit. Sometimes they don't have watches at all, most of the times just cheap watches. the only one where I saw nice watches was the BooksOff Super Bazaar 409 in Kawasaki Minatocho - I leave this information mostly for other people who live in Tokyo, but I don not suggest you to go there since it's in the middle of nowhere at 60-90min trip from any place you might be during your stay in Tokyo
I’d say what you describe is common. Be aware it’s a slippery slope though. Now it’s an everyday watch and a nice watch.
Tomorrow everyday watch, office watch, nice watch. Diver watch. Dress watch.
In a year you are looking at a full watch box, and trying to come up to justifications not to buy that nice watch you just saw on WC
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