Hi,
There is a new Haneda Gardens connected to T3 ( Intl terninal)- Have not been but there are shops ( only open at 8am) but there is a 24hr hot bath facility that is open to non-hotel guests ( some baths are outside ( 12th floor roof)
Haneda Airport Garden - Ota City, Tokyo - Japan Travel
That might use some time before the shops etc open
Regards
TBS