Prayers in Kufa and Karbala
Question :

What are the rulings of the prayer of the traveler in Kufa and Karbala? Do they have the choice of offering full prayers? Is Najaf considered to be within Kufa?

Answer :

The traveler is permitted to choose between offering a full or shortened prayer in the “haair” of Imam Hussain (peace be upon him), and based on an obligatory precaution it is the place under the dome above the holy grave of the Imam and not beyond this area. This ruling does not include the city of Karbala at large.
As for Najaf, it is not within the city of Kufa, so this law does not apply and shortened prayers is obligatory on the travelers in Najaf.