Hmmm... I could be wrong but I thought the appropriate term for a gym you were a member of was a possessive pronoun. But now that I think about it I'm not sure.
I went to the gym this morning.
I went to my gym this morning.
The gym was closed due to a fire.
My gym was closed due to a fire.
The monthly rates at the gym are outrageous.
The monthly rates at my gym are outrageous.
The gym has a pool
My gym has a pool.
Screw it... I don't know now