Shaun J has found some of this, but here goes:
The newspaper mention from 1864 quoted below matches well with the enumerator's route in the sense that there are various Pandon place names.
Unfortunately this area of Newcastle is poorly covered in maps at NLS, with a huge gap between the 6 inch map of 1858 and the revised town plan of 1894. By the time of the latter map the All Saints area had been redeveloped and many of these places were gone. For example, at FindMyPast address search, New Pandon Street disappears after 1871.
However, Pandon Bank still exists today. Here is a map view with the early 6 inch map overlaid on a modern street map. On the old map Pandon Bank is unlabelled but aligns with the large 'A' of the All Saints label.
That's as close as I have been able to get to Travellers' Entry
https://maps.nls.uk/geo/explore/#zoom=17.2&lat=54.97254&lon=-1.60495&layers=257&b=osm&o=10020 August 1864: Newcastle Daily Chronicle
LOT 24. All that BLOCK OF FREEHOLD PROPERTY, comprising a HOUSE in Pandon Bank, with two entrances, occupied by Thomas Kennon, Ann Sloan, and John Shepherd; a HOUSE in New Pandon Street occupied by Agnes Ferguson, John Riddle and others; and a number of tenement DWELLING HOUSES and a BAKEHOUSE, between the said houses in Pandon Bank and New Pandon Street, and forming the north side of the "Travellers' Entry in the respective occupations of Isabella Dixon, Joseph Main, John Travers, Terrence Timmins and others.
