Greenback Saloon.

[MajGenl.Meade]

FWIW whitehousehistory.org agrees that the Greenback "flanked" the theatre on the opposite side to the Star:

"Ford’s Theatre was flanked by bars, restaurants, and similar commercial houses. These included both the Star Saloon, a dram shop adjacent to the theater that would play a significant role in the Lincoln assassination, and the Greenback Saloon. Lincoln’s coachman, Francis Burke, and his miscreant bodyguard, John F. Parker, as well as his murderer, John Wilkes Booth, all had drinks at the Star the night of Lincoln’s assassination. James P. Ferguson, owner of the Greenback Saloon that flanked Ford’s on the opposite side, witnessed the assassination from the audience".