Upvote:5
There's no need to stay in Haneda, you already hold a valid Japanese visa so you're free to leave and come back for your flight later, once you clear immigration. Not sure where you're planning to go, but it could take you anywhere from 30-50min from Haneda to the city itself, so make sure to factor that in.
In case you're wondering what to do with your luggage, there's plenty of coin lockers in the airport and just about any sizeable subway station in Tokyo.
There are shower facilities on the second floor in the arrival lobby in Haneda, they cost about 1000 yen (approximately 10$) for 30min and provide you with what you need (towels, shampoo etc)
Upvote:8
The procedure for arriving and domestic-connecting passengers in Japan is the same. Everyone clears immigration and collects their bags for a customs check at their first entry point. Bags are only labelled as far as the first Japanese airport. After leaving immigration and customs in Haneda you will already be on the public side of the airport facing the exit to the street. You are in Japan now, you can walk out of the airport if you like, or you may turn right and follow the signs for domestic flights.
Since you are a connecting passenger it should be possible to check-in your bags for the domestic flight as soon as you arrive. This will save you from carrying them around. There are special check-in desks in the international arrivals hall that can handle this. Follow the signs for domestic flights: turn right out of arrivals and walk along the corridor to the far end. If this is not possible because you are too early (sometimes the desk is closed) then you can use the regular check in desks in the domestic terminal later.
There is bus over to the domestic terminal behind you when you are facing the bag check desk. The staff may invite you to use it. But do not use this, because it will take you through security and back into the airport.
There are airport lounges in the domestic terminal but they are not the place you want to spend more than a few minutes.