What county is Nottingham in?

Nottinghamshire.

Nottingham is within Nottinghamshire is everyday parlance. However, if you are being pedantic and technical ~ it is not.

In 1449 the then Borough of Nottingham received a Royal Charter. The Charter provided that the Borough of Nottingham with the exception of the Castle and Shire Hall was made in "all things separate and distinct of Nottinghamshire for all eternity".

The Borough became styled as the "Borough of Nottingham & County of the Same Borough". Nottingham acquired its own Coroner and Lord Lieutenant. The Courts were separated from those of the County. In essence Nottingham became its own County distinct from Nottinghamshire.

In 1897 Queen Victoria made Nottingham a City. The City Charter declares that Nottingham is to be styled and known as the "City of Nottingham and County of the Same City" for all eternity. Close examination of some War Memorials in Nottingham clearly draw distinction between Nottingham and Nottinghamshire as though they were separate counties.

In 1974 the City of Nottingham was effectively downgraded to being a District of Nottinghamshire. For the first time since 1449 Nottingham's affairs were meddled with by the authorities of neighbouring Nottinghamshire. In 1998 the City achieved Unitary Status. Birth. Death and Marriage Certificates issued in Nottingham refer to it being the "County & City of Nottingham".

The short answer is in informal chat Nottingham is in Nottinghamshire. If you are being correct and formal Nottingham is its own County.