Tokyo's indoor culture is the deepest of any city I know. The depachika basements, the multi-floor bookstores, the museum cafes, the converted warehouses: there is more good covered space here than you can use in a year. When the rain settles in, these are the places I send people who want a date that holds up for four or five hours without ever stepping outside.
Daikanyama T-Site for a slow afternoon
T-Site, the Tsutaya bookstore complex in Daikanyama, is the obvious answer for a reason. Three connected buildings full of books, music, and a magazine section in the middle that has titles you will not find anywhere else in the city. The Anjin lounge upstairs lets you sit with a drink and any book from the floor.
The move is to give yourselves an hour to browse separately, then meet in the lounge with two books each that you want to show the other person. This is a date disguised as a bookstore visit, and it works almost every time. Spend: about 1,500 yen each for drinks, free if you only browse.
The Mori Art Museum on a Friday night
The Mori in Roppongi Hills stays open until 10pm most nights, which makes it one of the few museums in the city you can use as an evening date. The exhibitions are usually contemporary and reliably good, and the same ticket gets you onto the Tokyo City View observation deck, so you get an art show and a skyline at night for one price. Tickets are around 2,000 yen each.
After, the restaurant floors of Roppongi Hills have enough range that you can decide based on mood. Avoid the chain places on the lower levels and aim for the smaller restaurants on the upper floors.
Ginza Six and the rooftop garden
Ginza Six is a department store that takes itself seriously enough to be worth a rainy afternoon. The Tsutaya on the sixth floor is enormous, with a focus on art and design, and the rooftop garden is technically outdoors but covered enough on most sides to use even in light rain. The basement food hall is one of the best in the city.
The rhythm is browse the bookstore, eat your way through the basement, sit on the rooftop with whatever you bought. Two to three hours easily. Total spend for two: 3,000 to 4,000 yen depending on how much you eat.
A long lunch at a hotel lobby lounge
Tokyo hotel lobbies are some of the most underused date spaces in the city. The Palace Hotel lobby lounge near the Imperial Palace, the Aman Tokyo lobby on the 33rd floor of the Otemachi Tower, and the Peninsula afternoon tea are all worth the price for a long rainy afternoon. The Aman lobby in particular, with its wood and stone interior and view over the palace gardens, is one of the most beautiful indoor spaces in the city.
Tea or coffee runs 1,500 to 2,500 yen per person, which is more than a cafe but buys you two or three hours in a room you cannot get into any other way.
A movie at Bunkamura plus dinner upstairs
Bunkamura in Shibuya has a small cinema, Le Cinema, that plays mostly European and smaller Asian films, and the building also houses a museum, a concert hall, and a few restaurants. You can see a film, eat at Les Deux Magots Paris in the lobby, and never deal with the Shibuya street chaos at all. The cinema is being renovated periodically, so check the schedule, but the building as a whole works as a rainy day plan.
A pottery or cooking class
The casual workshop scene in Tokyo is large and accessible to beginners. A two-hour pottery class at a place like Yu-Nakameguro runs about 4,500 yen per person and gives you something to take home a few weeks later. Cooking classes at places like Tsukiji Cooking on the edge of the old market area do sushi or ramen sessions for similar prices.
The value of these as dates is not the pottery or the food. It is that you spend two hours doing something with your hands while talking, which is a different texture than sitting across a table. For a third or fourth date, this lands well.
A neighborhood arcade and a yakitori dinner
The big Taito and GiGO arcades in Shinjuku and Akihabara are loud and bright and a different kind of fun on a rainy night. Forty minutes of UFO catchers, purikura, and the rhythm games on the upper floors costs maybe 2,000 yen between two people and is a useful palate cleanser if your dates have been getting too serious.
Follow with yakitori somewhere quiet. The contrast does the same thing the kissaten-after-Shinjuku trick does at night. Loud, then quiet, then home.
The Shitamachi Museum and a walk through Ueno
Ueno Park has multiple museums under one roof effectively, and on a rainy day you can move between the Tokyo National Museum, the Shitamachi Museum, and the National Museum of Western Art with minimal time outside. The Tokyo National Museum's Honkan building alone is worth two hours, and the cafe in the Horyuji Treasures building is one of the quietest museum cafes in the city.
Museum admission runs 600 to 1,000 yen per person. Pick two, give yourselves a long lunch in between at one of the restaurants in the park, and you have a full afternoon that the rain actually improves.