What is the proper way to refer to my aging Aunt?

With time, usage changes, and language evolves to better suit our circumstances. At present, there is really no proper way to address the elderly! Baby boomers, those who popularized yoga and fitess, vitamins and life extension, certainly do not wish to be referred to as 'old', far moreso than those before them, their predecessors who did not know of these, and accepted "old age" as a stage of life.

Patient-postive language dictates that we state that we are referring to a person, not simply a condition, reduced to an object or malady. Therefore, we include "person", as in "older people", "elder person, or "advanced-age person", or whatever other way we choose to describe the individual. Alternatively, within the medical setting, we would use "client", "patient", "resident", or even "consumer" at some facilities. But under no circumstances is it considerate, or professional, to refer to a person in this age group as simply "old", "geriatric", "elderly", or "senior."

Is "geriatric" even OK anymore?

Not really by itself, but if you make a compound word as above, it's better. Still, it remains widely used, and the etymology is from Ancient Greek ("old age"), so we continue to use it here due to its widespread usage in the medical community since the 1920s.

(Oh, and by the way, here are some other ones: Assisted-Living Facility is now an Assisted-Living Community, Home, or House. A Tour is now a visit. A patient is now a resident, consumer, or client. Elderly is now elder. Long-term care is now Senior Living. Bed or Unit is now Room or Suite.)