Oldest city

Damascus (population 6 million), the capital of Syria, is purportedly the oldest continually inhabited city in the world.

Jericho near the Dead Sea

Jericho is a pretty good answer, as it was one of the first cities established in the Middle East, probably around 8,000 BC.  However, the ancient city is a mile or so away from the modern city, plus there were several extended periods where it went uninhabited.

But whether or not Jericho counts, the oldest continuously occupied city that I'm aware of is Tallahassee, Florida.   It was the site of temple mounds, temples and dwellings starting perhaps by 10,000 BC.   It was inhabited by native tribes until Europeans arrived.  It was inhabited by both natives and Europeans for a while, but the natives eventually had to abandon it due to European diseases.  Since then it's been inhabited primarily by European descendants.

Jericho and Damascus claim it.

http://www.jericho-city.org/historical.html

http://www.tribuneindia.com/2002/20020623/spectrum/travel.htm

But one thing should be remembered. The Rig Veda
of the Hindus, now accepted to be 8000 years old,
is the oldest manuscript in the world. Mohenjodaro
in the Indian sub-continent is the oldest planned
city with high technology infrastructures for
water supply and sewerage.

The Indians claim that Kasi is the oldest city
oldest city in the world. Hinduism is the oldest
surviving religion of the world.

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

"The oldest University of the world was founded at
Taxila, where taught the great grammarian Panini."

ttp://ccc.1asphost.com/hamidsaeed/darood/HIST-PAKISTAN.htm