General:
* Dispensary
* Health center
* Medical center
* Outpatient facility
* Surgery center
* Treatment center
More specific:
* Ambulatory care center (focuses on providing care to patients who are not hospitalized)
* Infirmary (typically associated with schools or institutions)
* Sanatorium (historical term for a facility treating tuberculosis)
* Spa (for wellness and beauty treatments)
Informal:
* Doctor's office
* Practice
The best synonym to use will depend on the specific meaning and context of "clinic" in your sentence.