Where is the St Peter Basilica?

Answer

St. Peter's Basilica (see below for the distinction) is located in Vatican City, a "sovereign city-state" (essentially an independent country) located entirely within the greater metropolitan area of Rome, Italy. See the Wikipedia entry "Vatican City" for more.

Many people mistake St. Peter's for a cathedral, but it is not the seat of a bishop; the Cathedral of Rome is San Giovanni Laterano.
Find out more about St. Peter's Basilica at http://vaticanart.net/st-peters-basilica-architecture