If you value living space, you'll be happiest out of NYC.
But if you value meeting a lot of cool people, great things to see and do, great mass transit, etc then NYC is great even at a lesser overall level of purchasing power.
Am I as happy as I was in Boston? No. There's some perks (garage to park my motorcycle and a room for my office) but that's about it. Oh, and things are just easy here. No traffic, the DMV's 'bad' waits are 30 minutes, not 4 hours. That type of thing.
Meeting cool people happens much less frequently here, and the culture (even around OSU) is simply as not as academically focuses as hanging around Cambridge.
Purchasing power way up. Quality of life? A draw at best, probably a loss. If I had my way, I'd be back in Boston tomorrow.
Just taking a rude guess here (sorry if I'm wrong) but it sounds like you might be making a sacrifice for your family or partner? If so, you need to factor in how much they mean to you into your quality of life score for Columbus vs living alone in Boston. (I'm not judging you - a lot of us are in a similar situation!)