**Core Concept**
The patient's symptoms suggest a lesion affecting both the oculomotor nerve (cranial nerve III) and the cerebellum. This combination of ipsilateral third nerve paresis (weakness of the eye muscles) and cerebellar ataxia (uncoordinated movement) points towards a midbrain lesion. The midbrain is a critical area where these two structures are closely located.

**Why the Correct Answer is Right**
The correct diagnosis is likely a midbrain infarction or stroke, which involves the red nucleus, the oculomotor nerve nucleus, and the superior cerebellar peduncle. The red nucleus is responsible for coordinating movements, and its damage can lead to cerebellar ataxia. The oculomotor nerve nucleus, which controls eye movements, is also located in the midbrain, explaining the ipsilateral third nerve paresis. The superior cerebellar peduncle, which carries cerebellar output, is also affected, contributing to the ataxia.

**Why Each Wrong Option is Incorrect**
**Option A:** A lesion affecting the pons would more likely cause cranial nerve abnormalities, such as facial weakness or dysphagia, rather than cerebellar ataxia and third nerve paresis.
**Option B:** A lesion affecting the cerebellar hemisphere would cause ipsilateral ataxia, but not typically third nerve paresis.
**Option C:** A lesion affecting the brainstem would cause more widespread symptoms, including respiratory failure, rather than isolated third nerve paresis and cerebellar ataxia.

**Clinical Pearl / High-Yield Fact**
The "three-in-one" syndrome, characterized by ipsilateral third nerve paresis, ataxia, and hemiparesis (weakness on one side of the body), is a classic presentation of a midbrain lesion, specifically a stroke or infarction.

**Correct Answer:** C. Midbrain infarction.