The Examiner Office in 1812

 Maiden Lane, Covent Garden

Unlike many of the publishing houses of the day, which operated out of the infamous Fleet Street, the Hunts' Office was very near the hub of theatre (Drury Lane, the Strand, etc.), which would have been quite convenient to the writing of the Theatrical Examiner; they would have been saturated with theatrical gossip and just a stone's throw away from performances.

 Greenwood's Map in 1827:

Covent Garden (middle and left)  vs.   Horsemonger Lane (bottom right corner)

Contemporary, Color-coded maps: