This page suggests this tavern was at the corner of Russell Street and Brydges Street, which is now Catherine Street.
The overlays that highlight 17th century London features are approximate and derived from Wenceslaus Hollar’s maps:
Open location in Google Maps: 51.512822, -0.120882
The Rose Tavern stood in Russell Street, Covent Garden adjoining Drury Lane Theatre. Part of it was taken down in 1776, when Adam, the architect, built a new front to the former theatre for Garrick, then about to part with his patent. In Charles II's time it was kept by a person of the name of Long (buried at St Paul's, Covent Garden, August 5, 1661) and afterwards by his widow. Tavern tokens of the house still exist.
---London, Past and Present. H.B. Wheatley, 1891.
Chart showing the number of references in each month of the diary’s entries.