The Globe Theatre and the Swan Theatre

The Globe Theater was situated at Bankside in Southwark, London

Southwark.…in a section called Bankside.

In Southwark, south of the River Thames across from the City of London. The place where it was built is now called Anchor Terrace, Park Street, Southwark.

Shakespeare's Globe Theatre is the name of the reconstruction built in 1997. It is in the area of greater London south of the Thames, called Southwark. Its address is 21, New Globe Walk.

The theatre Shakespeare worked in was just called "The Globe" (no "Shakespeare's" about it) and was also in Southwark not far away. Specifically, the foundations are under 67-70 Anchor Terrace, Southwark.