@Sleep Near
Blagoevgrad is a good option, and I very much second your recommendation to be in/near a bigger city. Healthcare is possible anywhere, but it's much easier when you can easily access city services.
We very much like Plovdiv as it's a wonderful small city, and we have a great quality of life here. Not only does Plovdiv have plenty of medical options, but it's an easy drive on the A1 to Sofia (for bigger/specialist hospitals and the airport). Also an easy drive to the Black Sea (same highway, east), and two mountain ranges (Stara Planina north and Rodopes south).
The health insurance for immigration is a cheap emergency policy. It's recommended to get a proper private health insurance. The public system is accessible for non-EU citizens if you work (employed or self-employed), or you can wait 5 years for PR and then join.
I'm not sure that comparing Bulgaria with the impoverished boondocks of America is an encouraging comparison! Who wants to move in with a bunch of Appalachian hillbillies? :-)
Bulgaria's poverty is relative to the EU, a very prosperous bloc. I'd say much of the visible signs of poverty (for a foreigner) is down to the architectural style. For example, the Communist era panel blocks (common throughout Eastern Europe, not just Bulgaria) look a bit tatty and slum-like, especially if you come from Germany, Switzerland, USA, etc. But mostly they're not slums, and they're perfectly nice places to live (I also have a panel apartment).
Much of Bulgaria's poverty is within the Romany/"Gypsy" communities, and within the older/retired population (Bulgarian pensions are feeble). Many older folks live in Bulgarian villages (the trend is older, with youngest going to the big cities), which makes villages, relatively speaking, extremely poor. But the "vibe" in Bulgaria is way different from hanging out in Arkansas or Detroit, even in a country village. In particular, safety/crime here is, overall, very good. In most countries/locations, if you chase poorer areas (for cheaper property/living), the trade-off is crime and personal safety. Bulgaria is so great for expats precisely because it's one of the rare places that has low living/property costs, but is also safe and civilized.
I've lived all over the world, and I'd never say that Bulgaria was the "best" country. While it has many positives, it's a long way from being the best! However... in terms of bang-for-my-buck, Bulgaria is one of the best (if not the best) options around.