Formal:
* Je réside à Washington, dans le nord-est de l'Angleterre. (This is the most formal and literal translation.)
* Je vis à Washington, dans le nord-est de l'Angleterre. (Slightly less formal than the first option.)
Informal:
* J'habite à Washington, dans le nord-est de l'Angleterre. (This is a more common and casual way to say it.)
* Je suis à Washington, dans le nord-est de l'Angleterre. (This is a more concise and informal way to say it.)
Using a region name:
* Je vis dans le comté de Durham. (If Washington is specifically in County Durham.)
* Je vis dans le Tyne and Wear. (If Washington is specifically in Tyne and Wear.)
Remember:
* "Washington" is the name of a town, so it should be capitalized in French.
* "Nord-est" is hyphenated in French.
* "Angleterre" should be capitalized in French.
You can choose the option that best suits your needs and the context of the conversation.