So today Rob has been a great host. After making breakfast burritos and great coffee we visited Phillip and his family on Second Mesa; the cultural centre; and paid a visit to the Navajo hosted Pow Wow at White Cone. All in all a very interesting day.
As for front tire problem, I thought (at least Google gave the impression) that there are bike shops in Tuba City, but this is not the case. Of course this erroneous though is compounded by the fact that in my mind a city is a large metropolis, which is not the case in the USA, where even one horse towns often include city in their name!
Anyway, the upshot is that it looks as though a trip to Flagstaff is required to get new tyre! Otherwise it is 300 - 400 miles from my present location to the next bike shop on route. I am not convinced the tyre will hold out long. So Flagstaff it is!