Hypertensive Emergency with Posterior Circulation Stroke: The patient presents with severely elevated blood pressure (256/121 mmHg), symptoms of giddiness, blurred vision, and changes in color vision, along with impaired horizontal gaze and multidirectional nystagmus, which are indicative of posterior circulation involvement. The acute onset of these symptoms, especially in the context of uncontrolled hypertension, supports this diagnosis.

Posterior Reversible Encephalopathy Syndrome (PRES): Given the patient's history of hypertension and the presence of visual disturbances, this condition should be considered. PRES is characterized by reversible brain edema, often associated with hypertension, and can present with similar neurological symptoms.
Brainstem Stroke: The patient's impaired horizontal gaze, nystagmus, and other ocular motor abnormalities could also suggest a brainstem stroke, which might not be directly related to the hypertensive emergency but could be a consequence of the elevated blood pressure.

Subarachnoid Hemorrhage: Although the patient does not have a thunderclap headache, which is a classic symptom, the sudden onset of severe hypertension and neurological symptoms necessitates considering this potentially life-threatening condition.
Pituitary Apoplexy: The patient's symptoms of polydipsia, polyuria, and visual disturbances could also suggest pituitary apoplexy, especially if there's an underlying pituitary adenoma. This condition is an endocrine emergency and requires prompt diagnosis and treatment.
Cerebral Venous Sinus Thrombosis: This condition can present with headache, visual disturbances, and seizures, and while less likely, it is critical not to miss due to its potential for severe outcomes if not treated promptly.

Wernicke's Encephalopathy: Although the patient does not have a history of alcohol abuse, Wernicke's encephalopathy can occur in non-alcoholic patients with malnutrition. The presence of nystagmus, ophthalmoplegia, and confusion (if present) could suggest this diagnosis, but it is less likely given the patient's background.
Mitochondrial Encephalomyopathy, Lactic Acidosis, and Stroke-like Episodes (MELAS): This rare mitochondrial disorder can present with stroke-like episodes, including visual disturbances and seizures, often with a history of developmental delays or myopathic features. The patient's family history of inherited neurological conditions might raise suspicion, but the lack of other characteristic features makes this diagnosis less probable.