Vestibular Neuritis or Labyrinthitis: Given the acute onset of dizziness and facial droop without obvious stroke on CT, vestibular neuritis or labyrinthitis is a plausible diagnosis. These conditions can cause sudden vertigo and may be accompanied by facial weakness due to inflammation of the vestibular nerve or labyrinth.

Transient Ischemic Attack (TIA): Although the CT scan does not show an obvious stroke, a TIA could still be a possibility, especially if the symptoms are transient and resolve quickly. TIAs are often referred to as "mini-strokes" and can cause similar symptoms to a full-blown stroke, including dizziness and facial droop.
Benign Paroxysmal Positional Vertigo (BPPV): This condition causes brief, intense episodes of vertigo triggered by specific head movements. While it might not directly cause facial droop, the severe vertigo could lead to a fall, potentially causing injury, including facial trauma.
Ménière's Disease: An inner ear disorder that involves vertigo, tinnitus, hearing loss, and ear fullness. The vertigo can be severe and might be accompanied by other symptoms that could be mistaken for or contribute to the perception of facial droop.

Posterior Circulation Stroke: Even if the initial CT scan is negative, a stroke in the posterior circulation (which supplies the brainstem and cerebellum) can have subtle or delayed findings on imaging. It's crucial to consider this diagnosis due to its potential for severe consequences if missed.
Multiple Sclerosis (MS) or Acute Demyelinating Syndrome: Although less common in a 75-year-old, MS or other demyelinating syndromes can present with a wide range of neurological symptoms, including vertigo and facial weakness.
Cerebral Vasculitis: Inflammation of the blood vessels in the brain can cause a variety of symptoms, including stroke-like episodes. Given the patient's HIV status, there might be an increased risk of certain types of vasculitis.

Ramsay Hunt Syndrome Type 2: Caused by the varicella-zoster virus, this condition can lead to facial paralysis and vertigo due to involvement of the geniculate ganglion. It's less common but should be considered, especially in immunocompromised patients.
Superior Canal Dehiscence: A rare condition where there is an abnormal opening in the bone overlying the superior canal of the inner ear. It can cause vertigo and imbalance, among other symptoms, but is less likely to cause facial droop directly.
Chiari Malformation: A structural defect in the cerebellum that controls balance can cause vertigo and other neurological symptoms. However, it's typically diagnosed in younger patients and might not directly cause facial droop.