It's difficult to say as most of Europe's cities have been continually inhabited for millenia. But it seems Plovdiv, Bulgaria is accepted at the oldest city.

Plovdiv or Philipopolis in Bulgaria..is the oldest one.

Amesbury in the U.K. has been continuously inhabited since the 8th millennium BC

Provadia in Bulgaria has been continuously inhabited since 4700 BC

Argos in Greece has been continuously inhabited since the 5th millennium BC

Athens, Sparta, Olympia, and Rome

List of cities by time of continuous habitation:

http://en.wikipedia.org/wiki/List_of_cities_by_time_of_continuous_habitation

London, Rome and many others.......