My husband is flying from L.A. to Haneda, arriving at 3 pm on March 12. I’m flying from Bangkok arriving that same day at 5:30 pm. The next morning we’re flying to Hiroshima, probably leaving at 9;20 am. (How far in advance do you have to be at the airport for a domestic departure?) We are debating where to stay at or near Haneda. One possibility is Villa Fontaine Grand Haneda Airport, which is right at the airport (no need to take any transportation to get there). However, I am wondering whether there is enough to do in the area, or whether you are basically trapped at an airport. Other possibilities I’m considering are Keikyu EX INN Haneda and Keikyu EX INN Haneda Innovation City, which each entail a short bus or monorail ride but seem to have more things around and are less expensive than the Villa Fontaine Grand. These two look very similar. Is there a reason to favor one of them over the other? Which of the three would you recommend?

I would recommend considering Keikyu EX INN Haneda or Keikyu EX INN Haneda Innovation City over Villa Fontaine Grand Haneda Airport. Both options are conveniently located and offer easy access to the airport through a short bus or monorail ride.

These locations are so close to each other that I see no advantage one way or another. None of them put you in an interesting neighborhood or give you so much more convenience.

With late afternoon, early evening arrivals once you clear immigration and customs plus an early morning next day departure, I would choose ease and convenience. For me that would mean an airport terminal hotel (Royal Park, Excel or Villa Fontaine), which one depending on your departure terminal.

To curiousgeo's point, I would not underestimate the amount of time it could take to enter Japan. We arrived at Haneda from Chicago one evening last month, and it took over an hour to clear immigration and customs.

FWIW, we were on a overnight connection as well, headed to Saigon, with our flights in and out of Terminal 3. We stayed at the Villa Fontaine. It was so convenient to be able to walk there and not have to find additional transportation after a 12-hour flight and that long immigration line.

Another overnight connection here, to Singapore, made simple by a stay at the Royal Park.

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For your situation, here are some suggestions. If you value the utmost convenience of not having to take any transportation after a long - haul flight, the Villa Fontaine Grand Haneda Airport is a great choice. Although it might feel a bit like being 'trapped at the airport', most modern airports have a variety of amenities these days. Haneda airport has numerous shops, restaurants, and even some cultural exhibits that can keep you occupied for a few hours in the evening.
If you'd like to explore a bit more and save some money, between the Keikyu EX INN Haneda and Keikyu EX INN Haneda Innovation City, the main difference might be their proximity to different local attractions. Check online maps to see which one is closer to things you'd like to do, like local markets, small parks, or other points of interest. Generally, if you're arriving late and leaving early, the main consideration might be the ease of getting to and from the airport. In this case, look into the frequency and operating hours of the bus or monorail. If one has a more convenient transportation schedule for your arrival and departure times, that would be the better option.
As for domestic flights in Japan, it's advisable to arrive at the airport about 60 - 90 minutes in advance. This gives you enough time to check - in, go through security, and find your gate.
Overall, if you're really tired from the flights and want the simplest option, go for Villa Fontaine Grand. But if you're up for a bit of exploration and cost - saving, carefully assess the transportation and local attractions around the two Keikyu EX INNs to make a decision.