Tokyo's rainy season, tsuyu, runs roughly from mid-June to mid-July, and then typhoon season picks up the slack through September and into October. If you only date in this city on sunny days, you barely date in this city at all. The good news is that Tokyo is built for rain. The trains are covered, the basements are deep, and entire neighborhoods are essentially indoor.
Use the underground city
The stations themselves are dates if you know how to use them. Tokyo Station's Yaesu side has a basement maze called Tokyo Character Street and Ramen Street that you can walk for an hour without going outside. The Marunouchi side connects directly to the Marunouchi Building and the Shin-Marunouchi Building, which both have full restaurant floors with views and you never have to open an umbrella.
Shinjuku is even more extreme. From Shinjuku station you can walk underground to Shinjuku Sanchome, hit the Isetan basement food hall, come back through Lumine, and end up at a movie at the Toho cinema in Kabukicho without ever stepping into weather. This sounds dystopian. It is actually pleasant, especially when it is pouring.
Department store basements are real dates
The depachika at Isetan Shinjuku, Takashimaya Nihombashi, or Mitsukoshi Ginza are not just food halls. They are tasting tours if you treat them that way. Pick three things each, find a bench or take it back to a hotel lobby, and eat slowly. A good wagashi from Toraya, a piece of fish from one of the deli counters, and a single perfect strawberry from Sembikiya is a better dinner than most restaurants will give you on a rainy Tuesday.
This works as a date because it has a structure. You walk together, you each pick, you compare. It is low pressure and the conversation writes itself.
Museums that are actually good in the rain
TeamLab Planets in Toyosu is the obvious answer, and it works, but you have to book ahead and you will be in line with other couples doing the same thing. The Nezu Museum in Aoyama is a better date in bad weather because the building itself, designed by Kengo Kuma, is the point, and the garden looks better wet than dry. The cafe in the back overlooks the garden and is one of the quieter places in that part of the city.
The Tokyo Photographic Art Museum in Ebisu Garden Place is another good rainy day move. It is smaller than you expect, the shows rotate often, and Garden Place itself is covered enough that you can spend the whole afternoon there without getting wet, including dinner at one of the restaurants on the upper floors.
Kissaten weather
A kissaten is an old-style Japanese coffee shop, usually run by one person, often smoky, always slow. Tokyo still has hundreds of them, and rain is exactly the right reason to find one. Saten in Koenji, Cafe de l'Ambre in Ginza (which has been roasting coffee since 1948), and Chatei Hatou in Shibuya are the canonical ones. Hatou serves coffee in cups the owner picks for you based on what he thinks of you, which is either charming or alarming depending on your mood.
The move is to bring a book each, sit across from each other, and only talk when you feel like it. This is a date that respects the weather instead of fighting it.
Onsen day trips that are actually close
If the rain is going to last all weekend, leave the city. Hakone is ninety minutes on the Romancecar from Shinjuku, and a rainy onsen is significantly better than a sunny one. The steam reads better, the views from the rotenburo at places like Tenzan in Yumoto feel earned, and the train ride back through the wet hills is one of the best parts.
For something closer, Spa LaQua at Tokyo Dome City is a full onsen complex inside a building, twenty minutes from Shinjuku, and you can spend six hours there for under three thousand yen each. It is not glamorous. It is exactly right for a typhoon Saturday.
Movie theaters worth the trip
Most Tokyo cinemas are fine. Two are better than fine for a date. Bunkamura Le Cinema in Shibuya plays smaller European and Asian films with reserved seating and a quiet lobby. Theatre Image Forum in Aoyama runs documentaries and experimental work, and the cafe upstairs is a reasonable place to talk afterward.
The rule for movie dates in Tokyo is to pick the cinema first and the movie second. The wrong cinema with the right movie is worse than the right cinema with whatever is showing.
What not to do
Do not try to do an outdoor plan in light rain and tough it out. Tokyo rain turns heavy without warning, and being soaked in Harajuku at 4pm with another hour to fill is grim. Either commit to indoors or commit to the rain as the theme. Walking the Meguro River with one umbrella between you is romantic. Walking the Meguro River pretending it is not raining is just wet.