Depends how formal the language is. In normal speech use just "gynaecologist's".

If you really want a word for the premises where a gynaecologist practises, then "clinic" is the most appropriate (as in "gynaecology clinic" or possibly "gynaecologist's clinic" if you are thinking more of the doctor than the premises).

Usually doctors have surgeries (even though no surgery is performed there) but this is not used for gynaecologists.

In US English, the gynecologist's office is simply the entire complex where a gynecologist practices, including receptist office, waiting room, etc.

I think this is referring specifically to the room where the examination is held, which would therefore be called the examination room, or in colloqiual usage, the exam room. This term is often used to describe the room where gyn exams take place in a hospital.

So more context would be useful.

For tons of examples, google "gynecological exam room".