Hi,
I'm a Columbus Ohio local, and a caregiver to my elderly mother. Hats off to you for helping from afar; it is not an easy thing to do!
My mom had been disabled for the past 20 years, now nearing 80 years old. She went through breast cancer treatment over the past 2 years through Ohio Health hospitals (mainly Grant Hospital, Riverside Hospital and Doctors Hospital). She has always lived on the West side of town, close to Doctors Hospital.
At times over the past 20 years, she has utilized a service called Senior Options, which coordinates transportation to medical appointments, Meals on Wheels, and a few other services. Costs are on a sliding scale based on income. You need to reside in Franklin County. We had some issues when her main physician moved to Westerville just over the county line - the transport services were unwilling to travel outside the Franklin County area.
Here is a great resource for all things senior-care in Central Ohio - links to Senior Options are on this site as well.
http://www.coaaa.org/If the medical appointments are the most frequent trip, I would recommend living west of I-71/315 and north of I-70. OSU is centrally located right on 315 and north of 70. Riverside is a few miles north of there off 315. Columbus is a boom town, and traffic and construction are awful everyplace. I live and work near Grandview Heights (close to OSU), and travel to Canal Winchester for my cycling club at rush hour during warm months. I highly recommend avoiding this commute! Assuming you don't need to travel to SE Ohio at rush hour for family visits, you will save so much time during your daily life living close to your most frequent trips. If you visit family once a week duing non-peak hours, the added time from NW Columbus to Canal and beyond will be minimized.
A second choice as someone mentioned would be the west side in general. I live 2 miles west of Upper Arlington in an area with Columbus taxes, but super close to UA, Grandview, Hilliard and all highways. I avoid the insanity of the horrendous East-West traffic, but I am near most things in my daily life. My forays to Canal Winchester are much less frequent, so I endure the gridlock on 33 minimally. In the Columbus/Hilliard area, you may find a bit lower rents than closer to OSU or Upper Arlington (near Riverside).
Feel free to reach out if you need more info or advice, and best wishes to your father on his recovery!