A dirty bomb would certainly not render an entire city and surrounding land mass uninhabitable for thousands of years.
It would dirty up a few blocks, depending on the size of the conventional explosive and the wind.
It would still be cause to level a few cities in the mideast though.
Plutonium 239 half-life is 24,000 years. Plutonium 244 half-life is 82,000,000 years. I'd say that was long enough to dirty up a city.