Would anyone be set on a specific Western chain or using points? If not, then 3/2/2 at a Japanese business hotel chain might be easier. I'd suggest a room size of at least 22-24 square m for 3 people, for ~ 3 days if people mostly travel with 1 medium size checked bag. Larger room is nice if the budget allows and also ime, prudent if staying 4+ nights or doing more shopping.

Took a look on Google Travel hotels for 3 guests as that'll be the harder to find as a true triple (no one on a couch "bed"), though you want to check bed sizes & requirements in the details - will anyone be sharing a bed or does everyone prefer their own? Anyone extra tall, need Western levels of bed cushioning, or unable to get off tatami/bunks? Japanese chains usually have harder beds and some of the apartment hotel rooms have 2 pushed together twins + 2 bunks which may not be great for mobility challenged or larger people (probably thin mattress, might not be long enough). If people have not traveled together recently, do they need to avoid any weird bathroom setups like sink in bedroom or transparent/window from room to bath (yes, those pop up sometimes)?
https://www.google.com/travel/search...fCm7QYsemFAMAE

Booking.com on Desktop browser also shows the bed options from the search results so you don't need to click into everything. If you can narrow it down to a handful of hotels closer to the desired price range, then you can run a best price search from Google or other places. I would book direct, though, since you really need specific room types & OTAs sometimes get the inventory/booking wrong.

If someone really wants to use points or stay at a western chain/Park Hyatt Tokyo, it's a bit out of my expertise with 4 months advance search for < $800/nt for 7 people. It might be a case of having one party book the bucket list hotel and the other staying nearby at a more affordable chain or the frequent flier using their points for everyone to make the budget work out.