Which state offers the best and most services for elders?

I agree the county is the significant filter. My 2 elderly aunts in south FL live in a resource-poor county and are just 1 mile from a much better one. Something they didn't even think to consider when they moved there but that was in 1975 and lots can change in even just a few years.

There are benefits to living in a rural area but I think your best bet is a suburban one. Fewer people mean fewer taxes collected, which can translate into fewer resources and options. Metro areas have resources but also lots of demand. It's so admirable of you to think this deeply about it but it's all based on an idealized idea of how it will go for your Dad. No one can ever know what will transpire and what will be most valuable to him (and you as his caregiver).

Senior transport services sound great until you find out they won't accept anyone with cognitive issues unless they are accompanied. County provided In-home services sound great until you're in need and there's not enough qualified and experienced aids and it's not full-time, or he doesn't qualify. Meals On Wheels sounds great until your LO says the meals are gross and refuse to eat them (and they don't taste like home-cooked food...sorry that's what happened with my LO).

Maybe compare the states' Medicaid qualification criteria and look-back, or the number and locations of adult day care programs (and cost), how many Medicaid beds are in that county at quality facilities, how many reputable care agencies, healthcare proximity and accessibility, etc. Look for services that help the caregiver (you) as well as the receiver. In our case my MIL was in a suburban area and social services was very approachable and helpful -- more than I ever imagined they would be. She is in a great facility on Medicaid and even has a private room, which is very rare on Medicaid. I'm focusing on Medicaid because so many hard-working, financially responsible adults run out of money due to the cost of care. You can read about the great need right on this forum alone. Wishing you all the best as you research and plan ahead and peace in your heart no matter what is decided.

Please do not consider just the State but the area you want to move to.
Due to my Husbands dementia I/we moved from one County to another. Same State. And I have to say the County we moved to was much easier when I was looking for resources. The County we moved to was what I call Veteran Friendly and fewer people in the county made it easier to connect with the services we/ I needed in order to care for him safely.
So from the two States you are consider look into the various resources that would be available to you.
Also check Hospitals in each area. And if your dad, you or your husband is a Veteran see what resources there are that you might have to access at some point.

I can only guess that either SC or NC would be a better choice than NY, any day of the week, not only from a financial standpoint, but also from a weather and crime standpoint as well.
Now I live in NC(not Raleigh area, though my daughter is in that area with her family,) and in the city I'm in, we have a lot to offer seniors, from senior daycares, to lots of choices for senior living and care, to different activities designed just for seniors.
Your best bet may be to just "Google" both states to see what is offered for seniors in the areas that you're thinking about.
I grew up in Wisconsin, and was grateful to get the heck out of there, as I am not a fan of winter, so if you're a native of NY, and think you will miss winter and snow, then you probably don't want to live in either SC, or NC, as we seldom if ever get any snow, and if we do it's usually just a dusting.
I've lived here since 1991, and I have yet to own a winter coat. Now that doesn't mean that you may not occasionally need one, but for as little as you might, it's just not worth the investment, when a nice sweater coat or fleece lined jacket will do. Have fun on figuring out where you will be going. It will be quite the adventure.

Di27813, this is a good basis on which to analyze a potential move, but it does require a lot of research.    Many of the people here are still caregivers and have limited time, but still offer advice and opinions.  However, what you ask is to me a potentially complicated (assessing one state's offerings vs. another, the basis for assessment, etc.) and time consuming task.

However, those who may live in either SC, NC and/or NY could offer insights from their experiences and perspectives.    But you might want to share other issues of concern beyond the cost of AL.

What I would do is create a checklist of all factors that are important, including the cost of AL, and any follow-on placements.    I would also consider and evaluate the cost and array of home care, in the event it might be needed sometime in the future.

What else is important to you for your father's care?   Activities in each AL facility, closeness to hospitals, number and reputation of local hospitals, abundance or shortage of emergency vehicles for transport, medical firms in various practices (cardiology, orthopaedic, internists, etc.), PT/OT facilities in the event of physical injury and need for therapy, etc.   Is it important to be in an area with a teaching hospital?

In addition, I'd consider closeness of special restaurants your family may prefer and to which your father could be taken, religious institutions if that's important to him, senior center activities (as well as in an AL facility).   

Imagine what he would need, then research all the potentials.