Should you book a room for an early Tokyo arrival?
I'd book guaranteed room access for a Tokyo morning arrival when sleep, a shower or a child's nap is essential; if you only need to leave bags, I would keep the normal arrival-night booking. An early check-in request is not the same product as a room reserved for that morning.
Start with when you need the room, rather than the aircraft's landing time. Immigration, bags and the journey to the hotel sit between those two moments. I would pay for certainty when the first day depends on lying down, but I would not pay for an extra hotel night solely to avoid carrying a suitcase that the property has agreed to store.
When would I book the previous night?
I'd book the previous night when you need access well before the hotel's offered early check-in window. Before committing, the hotel needs the arrival date, local arrival time and a clear agreement that it will hold the reservation through that arrival. A booking beginning the night before can otherwise look like a guest who has failed to arrive.
I would ask for one continuous room assignment when the morning access and the remaining stay are booked separately. Paying for two reservations does not by itself promise that you can sleep through the change between them. For a family with bags and tired children, avoiding a second room move can be the reason to pay more for a properly arranged continuous stay.
What does paid early check-in actually buy?
The Villa Fontaine official FAQ gives normal check-in as 15:00 and offers paid early check-in from 12:00, subject to availability. Its Grand Haneda Airport row lists 3,300 yen per room per hour; the FAQ says access before noon is charged as a night's stay. These are that operator's published terms, not a Tokyo-wide rule.
For that example, I'd compare the quoted noon arrangement with a reserved previous night if you need several hours in the room. A fee schedule describes the cost when the service is available. It does not guarantee that housekeeping can release a room or that you can arrive at 07:00. I would not build a child's first nap around an unconfirmed request.
When is luggage storage enough?
I'd use storage when you can manage a quiet first day without room access. The hotel's written arrival instructions should establish whether it accepts bags before check-in, where they are held and when you can return. Do not assume an apartment, staffed hotel and unattended accommodation provide the same service.
Keep the first outing close to the hotel and easy to shorten. Breakfast, a neighborhood walk and an early lunch can fill the gap more usefully than a timed museum across the city. I would leave the expensive reservation for a later day, when a delayed arrival or fatigue cannot turn it into a missed booking. The first morning does not need to repay the cost of the flight.
Should you stay at Haneda or go into Tokyo?
I'd choose an airport room if you need rest before continuing and the reservation covers those hours. I would continue to the city when the hotel can solve the early access and most of your stay is there. An airport night followed by a city move creates another check-out gap; it is useful only when the rest outweighs that extra move.
Use the Tokyo airport transfer guide to compare the complete arrival route. A hotel at Haneda is not a solution for a Narita arrival simply because both are Tokyo airports. For a flight arriving late rather than early, the late Haneda arrival guide addresses the different problem of reaching the hotel after evening transport ends.
What would I confirm in the room booking?
I would put the local arrival time, guaranteed access time and continuous room arrangement in the reservation notes and obtain the property's agreement before choosing a restrictive rate. Then compare the full cost: previous night or early-access fee, transfers and the first night you would otherwise book. A cheaper rate that does not cover the required hours is not an equivalent option.
Choose the neighborhood for the rest of the trip, not just the first morning. The Tokyo accommodation guide compares the bases, while the family apartment-hotel comparison helps decide whether one room will work once everyone is awake. I would solve arrival separately, then keep the room that makes the following days easier.