Feb 15th stay in Tokyo. Love hotel or book a regular hotel in advance?
 

If you plan to check in early, I guess you'll find available rooms, but an ordinary hotel will likely be cheaper, since a Love Hotel will charge you a "rest" fee for the hours before 10 or 11pm and a "stay" fee from then until the morning. Also, I think it's probably easier to step outside for a meal or a stroll if you're staying at an ordinary hotel. My suggestion is to reserve a room at a reasonable hotel and take yourselves to a karaoke box for the trash culture experience.

As jib71 sort of mentions, it’s the going in and out of the hotel room that is the biggest inconvenience, when checking in, you don’t usually get a key, instead you find the door already open when you arrive - makes it difficult to pop in and out unless someone is left behind. Means you can end up having to ask permission/negotiate in order to go out. And that kind of cancels out the main appeal of getting a room somewhere like Shibuya or Shinjuku, which is usually considerably more expensive than a similar sized Love Hotel room in a more “downtown” area such as Asakusa or Ochanomizu.

But if that’s what you want, I just looked at the Agoda booking website and there were rooms for your night at under 12,000 yen at “Hotel The Hotel” in the Shinjuku Kabukicho area - involves checking in after 9pm and checking out after 10am.
I wouldn’t imagine you’d find anything much cheaper for a whole night, not unless you are willing to go to a less hip and happening area.

I didn't want to put it so indelicately.

Probably checking out before 10am. If the OP wants to check in during the late afternoon or early evening, or check out any later than 10am, I expect the additional hours might add 50% or more to that price.

I can't imagine a tackier, less convenient introduction to Japan than that in the OP.

Highly recommend just reserving rooms in a real hotel so you can see a little bit of Tokyo near-by.

Yes. BEFORE 10am. Thanks for catching that.

Friday nights tend to be really busy for love hotels, especially Shinjuku and Shibuya, for various reasons best not discussed on FT. In addition, love hotel beds, even though they are king size beds, won't fit three people sleeping, as there's only one bed per room. Also some love hotels don't allow you unlimited in/out privileges. You go in and you don't leave until your "business" is done, or you can prepare to pay for another room. That being said, some high end love hotels have those open baths and fancy bathrooms and what not.

OP, what is the exact timeframe of your 24hr layover?
If you're arriving early, as in morning, it may work out well for you to do the love hotel then check into the normal hotel for the night.
You should familiarize yourself with the concept of rest (kyukei), free time or service time, and stay.
It's not impossible to go out during your love hotel stay, but it's certainly not convenient for that and plus you'll need to be able to talk to someone in order to do that (that someone will likely not speak English). So a normal hotel would be a better option for much of the time that you'll have in Tokyo.
If you're really keen to check out a love hotel, I think it might be worthwhile.
There're so many different types of rooms out there including some that are quite frankly not much different than a business hotel room, and every place operates differently in terms of how to pay, rates/plans, hours of service time, whether service time is even available, etc. There are guidebooks in Japanese with pictures and all kinds of info, and those are really the best sources of info. You don't have that. Plus, if you have luggage, you'll have to do something about that. You probably want a really cool room, whereas a typical Japanese couple won't care as much and just needs something that's available at a reasonable rate. So I think you might need to end up doing a lot of research and planning and, in the end, you might find it's not really worth it.

Toyoko Inn Shinjuku Kabukicho Economy Double 9600 Twin 11100 per room per night double occupancy and complimentary buffet breakfast. Now they are fully booked for Feb 15 but there are usually late cancellations up till the day. You just have to keep checking.

A Toyoko Inn in the red light district with no available rooms reminds me of the joke "The food is so bad ... and such meager portions."

If david_oz really does want to do the whole Love Hotel experience, in Shinjuku, in his shoes, this is what I would do if I was booking right now for 15th Feb.

Get an “apartment” with G-Stays using booking.com. There is a free room that accommodates 3 people (double bed and a futon). It’s in the Shinjuku Kabukicho area right next to Higashi Shinjuku Station. The whole group can crash out there when they arrive, stash luggage and go eat, explore, whatever.
Later on, the third wheel can stay at the apartment and david_oz can go off with companion to find a love hotel room. If they are unsuccessful they have somewhere to go back to.
The 3 “bed” apartment is currently 15,000yen - they’d effectively be paying a 3,000yen surcharge for the option of having 3 people there instead of 1 or 2.

I would keep checking Rakuten or Jalan daily until the day of your stay to see what opens up. Many hotels offer special “day-before” rates to fill any empty rooms due to last minute cancellations.

LCUF seems to have misunderstood the OP’s initial questions.
I don’t think there is a blanket answer to whether three people are allowed in a room. Will depend on the room and the hotel.