The arrivals lounge is closed. There is a shower facility one floor down from arrivals after you clear immigration (I think 2F). It will be open at 6am and is free for arrivals in business class and ~1500 JPY if you need to pay. It doesn't offer anything besides showers. You can then go to Haneda Garden connected to the airport T3 or head into the city.

Though touristy and not the same as before the tuna auction relocation it is still fun to walk around Tsukiji early in the morning. You can lock your luggage in a locker at the station.