Formal:
* J'habite à Nottingham. (I live in Nottingham.)
* Je réside à Nottingham. (I reside in Nottingham.)
Informal:
* Je vis à Nottingham. (I live in Nottingham.)
You can also use the verb "demeurer" which is more formal than "vivre" but less formal than "résider":
* Je demeure à Nottingham. (I live in Nottingham.)
Important: In French, you need to use the preposition "à" (at/in) before the name of the city.