Currently hovering around The Knot, Keio Plaza, Citadine and Granbell.
No problem with The Knot (plenty of foreigners though
). Tthe rooms require keycards or PINs but not the elevators. The bathrooms (unit baths) are a bit dark, with only one light bulb near the top of the toilet side and not enough light in the bath/shower. It's also bit further away than other hotels you have mentioned as you need like at least 15 minutes walk from the JR station west exit, even further away than Park Hyatt Tokyo, and Park Hyatt Tokyo is already far from the JR station. No direct bus / shuttle bus although cheap by taxis (less than 1000 yen one way, since they started with 400 something yen now).
Keio Plaza rooms are nice and they have renovated the rooms for their main tower, a bit pricy, but again no keycards required to access the floors.
Hotel Gracery Shinjuku is one of my favorites and also nice, BUT keycards are required to access the floors. Personally I like their bathrooms (shower area plus proper bathtub for a business level hotel) so you and the girl can play there if you wanted to. Instead you can meet the girl near the lobby sofas or even the first floor hotel entrance (for shuttle bus and taxi) or the other entrances (one near 7-Eleven / Gindaco / Taiyou no Tomato Ramen restaurant, the other one near the elevator / escalator to the movie theater). The only downside to those alternate entrances are that the noisy mosquito sound they play all the time to keep people congregating near them.
Hyatt Regency Tokyo also doesn't need keycards for the elevators but the rooms are so old (WTF, get on with the times and renovate already) and very near Keio Plaza Hotel.
New The Hilton or the Granbell in Shinjuku. Neither requires keycards for the elevators, so your friend/provider can come directly to your room.
FYI if you are staying in Granbell Shinjuku on the 12F, you will need the keycard to enter the hallway to the rooms, as the floor has a restaurant on the other side. I stayed on the 12F with the double room and loft before so I can say for sure.