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Go to the doctor. Or

Go to the doctor's.
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The first is ok, the second needs 'office' at the end.
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Yes, I'd say it can.

And the other odd thing about this is that we use "the" even though we don't even know which doctor we might see.
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Comments  
Hi,

The construction you have in mind is usually used with shops or people's homes. I'm not sure about AmE, but it is used in BrE.

I bought it at the baker's.
I picked it up at the butcher's.

I saw her at Jack's.

I don't think it can be used with 'doctor', but it takes a native speaker to be sure. Emotion: big smile

Michal
 BarbaraPA's reply was promoted to an answer.
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Thanks GG,

I didn't know it went also with 'doctor'. I wasn't even sure it was used in AmE. Emotion: smile