I need to be in Town for a few days - I'll be staying at the club.
After my two meetings in the morning, I'll have a rest at the club before the three in the afternoon.
He's been in the club for several years, and he'll stay in the club for the rest of his life. [This refers to a simple social club - for example, a gardening club. And beware: 'in the club' can also mean 'pregnant'; so you have to be very careful that it's clear which club you mean if you say 'She's in the club'.]
*Since the mid '60s, there have been clubs that admit women members (and even - for all I know - women-only clubs). But in the hey-day of such establishments, their members were men.