I end up in Kokura/Hakata area often enough and used to date a girl from Fukuoka a number of years back so I did some pretty extensive research on couples-suitable (size, bed, good bath/shower room, etc.) rooms and there are a few very decent ones directly in front of Hakata Station on the main streets. JR runs a great chain called "The Blossom" hotels in Hakata with a good one right in front of the station. Same thing with Mitsui Garden Hotel. If you're going to stay in Canal City, where I'd imagine (if you're under 30) it'd be easier to try picking up younger girls as there's generally more younger person shit over there, there's a Dormy Inn Premium--this is my preferred hotel chain in Tokyo, Osaka and elsewhere due to the rooms, w/d units, rooftop onsen and a number of other amenities.
That all said, these being generally nicer hotels, I can't recall any that didn't require the key card to operate the elevator. You might have to slum it a bit if that's what you're after. I noticed there is a Hotel Club Hokke near Hakata Station, and I used to frequent the Osaka location often when I was younger and poorer (and it didn't hurt that Hokke was located in the Osaka NH district). If the Hakata location is anything like in Osaka, they don't even have hotel key cards yet and issue actual physical keys on lanyards that they ask you to turn in to the front desk staff every time you leave the hotel (which nobody actually does). I could've brought back every ladyboy in Toganocho and the staff at the front desk, which was located around the corner from the entrance, would never have known about it.