Oh man I love planning fun stuff!
Almost every weekend there's some event happening in the Yoyogi Park event space, those are always fun to go to.
Go to the Mystery Circus Escape Rooms in Shinjuku, they have at least 3 rooms in English (I've done one, it's fun even though we lost)
Do the Underground Metro Mystery (It's an all day event you can do on your own time and schedule with a partner, it will either make or break a relationship but I had a load of fun)
Go to the Jelly Jelly game cafe (as a double date) and play boardgames and drink (They have alcohol and you can bring your own snacks)
If you don't want to do Disney there's Tokyo Dome (With two spooky scary horror houses to hold hands through) or Puroland if you super like Kawaii things.
Also around Tokyo Dome is a science centre and planetarium!
Take a hike in Todoroki Valley (it's only a 20~30 minute walk if you're not one for hikes but want to do a bit of a romantic stroll especially in Sakura or Fall leaf season)
Do some touristy things like going to Asakusa, but to kick it up a notch you could take a boat ride to Odaiba afterward (Or start in Odaiba and go to Asakusa via the boat), or do a night boat tour. Or get very traditional and I can't remember the name but there's a place in Asakusa where you can learn to make some traditional hard candy that is in the shape of animals.
Go to a Sumo Match, and since you're in the area check out the Edo Tokyo Museum in Ryogoku. There are also tour plans where you can have dinner with some of the Sumo Wrestlers afterward.
Make a picnic and go to one of Tokyo's many beautiful parks or gardens. You can also rent a dog and play in Yoyogi park with a pup for a few hours if you need to work on picking up a date~
There are a couple places you can rent boats so if you feel like showing off your powerful rowing skills and manly muscles you can try that.
If you want to get hella drunk but in an interesting way there's the Kurano Sake Market which has hundreds of different sake, umeshou, and shochu to try. (I got super plastered there on a shared birthday with some friends because they had a chocolate sake that I mixed with a caramel sake and ooh that was DANGEROUSLY delicious.) You can bring your own snacks and this is a chain so there are a few around Tokyo so stop into a basement department store and grab a few bites of different foods to pair with all the different alcohols.
Outside of Tokyo there are beach dates if you wanna show off your hot bod and get a tan, Onjuku has a really nice beach and renting a hotel or air BnB for the weekend is fun. Or taking a daytrip to Narita and Narita Sensoji Temple and the super traditional shopping street leading up to it.
Or I mean there's Bowling, Billiards, Darts, and Karaoke which could all be found at a Anata no Warehouse which is a sight to behold in and of itself.
If no one has tattoo's then spending some time at Oedo Onsen is fun to end an Odaiba date.
Or the hundreds of weird cafe's/restaurants like Alcatraz, the Ninja Cafe, there's a vampire cafe, or high tea at one of the Alice in Wonderland cafe's.
Or even show off your cooking skills at ABC or Budda Bellies cooking studio's/classes where you'll learn to make something with your partner!
