Thanks for the responses so far. I have two additional questions about getting back to the gate after my tour of Narita:
One: If we miss the flight going on to Chicago (on United) what then? Will we face a huge fine to be rebooked, or might we have to wait for days in an expensive Toyko hotel until there is a seat in our fare class available? We are on super economy tickets.
Two: How do we get away from paying for the departure tax. I suspect to get past a certain point in the terminal going through passport control, etc., there will be a line asking for $ for the departure tax. If I would have stayed in the secure area, that line would not be an issue.
Three: When leaving terminal one on my way to tour the area I will have to go through passport lines and show a immagration card. Will the person reviewing my passport ask why I am leaving the airport area for such a short period of time, will they let me out of the terminal?