Looking at this map from 1921 (a later one in 1945 shows the same) the nearest school was on Leazes Lane, with the next nearest (in the other direction) at Snow St/ Douglas Terrace
The 1936 Ward's Directory Whitley Bay, Tynemouth, North and South Shields, Jarrow, Wallsend, Newcastle upon Tyne has the following likely info for the two locations:
Council SchoolsSnow St (J.H. Tweddle, master, Miss M.H. Bell, infants mistress)
Douglas Terrace
Non-provided SchoolsSt Andrew's C.E. (J. H. Chantler M.Sc., master,
Miss M.H. Youngson, infants mistress) Leazes Lane
EDIT - ADDED: forgot to add the link to where the map is to be found online
https://maps.nls.uk/view/101099345Boo