Depends on your definition of city. The most westerly CAPITAL city in Europe would be Dublin.
The most westerly City in Great Britain (England, Scotland and Wales) is St Davids in
Pembrokeshire, Wales.
St Davids was granted city status by Queen Elizabeth II in 1995.
Edinburgh
Belfast
Turo
Tut
oslo
Nicosia is the most easterly capital in the European Union, being in Cyprus, which is the most easterly country that is a member of the European Union.
The easternmost capital on the mainland of Africa is Mogadishu, the capital of Somalia.
Helsinki, the capital and largest city of Finland, is located in southern Finland on the shore of the Gulf of Finland. The Gulf of Finland is the easternmost arm of the Baltic Sea.
Papua is the easternmost province in Indonesia. It covers the western half of New Guinea and other closeby islands. The capital of Papua is Jayapura.
Russia is the easternmost country in Europe as it crosses into Asia.
Augusta, Maine
Rhode Islands Providence.
St. John's, Newfoundland
Rhode Islands Providence.
St. John's , Newfoundland
My guess is Wellington in New Zealand is both the southernmost and the easternmost capital city on earth. 41° 17′ 0″ S, 174° 27′ 0″
The country of Iceland has the westernmost and northernmost European capital city. The capital and largest city of Iceland is Rychivyk.