In Europe the inner city is often the oldest part of the town, which contains (unless destroyed by wars or conflagrations) many churches, half-timbered or classicist houses, market-places, shops, pedestrian precincts, narrow alleys, museums, operas, parliaments and a palace or two (depending on the town, of course :). Living there is expensive. The lower class lives in some hastly build-up suburbs.
Of course, if you rely on this description while visiting Europe, you will only find cities not matching it.