I had a very sore throat this morning, so I went to the doctors to get it treated.
My boss asked why I was absent yesterday - I told him that I was at the doctors.
Here, "doctors" implies the act of going to a clinic to see a doctor, so you don't need to mention it. Note, however, that clinic, more often than not, refers to a place (surgery) operated by one or more general practioner doctors (GP).
This is slightly different to hospitals and hospital doctors. If your illness gets escalated by your GP to a condition requiring hospital treatment, then the above would become:
I had a very sore throat this morning, so I went to the hospital to get it treated.
My boss asked why I was absent yesterday - I told him that I was at the hospital.