The pub at top right of the map: 1 o'clock, probably the King's Arms, 28 St James St, cnr of Kitchen St. Stephen McGrath was tenant in 1909 when it was owned by Peter Walker, later by Higsons. There were three licensees between 1/1/1900 and 1909.
At 2 o'clock, Royal Vaults, 1 Bridgewater St, cnr of St James's St. Manager William Pitcairn Sutherland, owners Harding & Parrington, later Walker Cain. There is a photo of this pub in "A Pub on every Corner" Vol. 1, Lpool, City Centre, by Freddy O'Connor.
Central: 37 Bridgewater St, cnr Simpson St [the map has this wrong as Sampson!] - White Cat, T.Lloyd tenant.
All this from the City of Liverpool Licensing Book for 1909, the only copy I have, but there is more information in the Liverpool Record Office.
D