Is Miss Emily unsympathetic as a character? Why?

On the whole, you'd have to say that Miss Emily is an unsympathetic character. Apart from the fact that she's a murderer, her whole demeanor suggests someone you wouldn't want to get too close to. To some extent, this isn't her fault; Emily's a product of a strict, sheltered upbringing. Her father hindered her development as an adult by scaring off any potential suitor. All things considered, it's not surprising that Emily turned out the way she did.
Having said that, she still needs to be held accountable for her actions and her behavior. Long before she finished off poor old Homer Barron with a dose of arsenic, she was a deeply unpleasant character, routinely treating the townsfolk with arrogant disdain. But then, the good people of Jefferson didn't exactly help matters by venerating Miss Emily as if she were some kind of historical relic, a symbol of a vanished past. Though Miss Emily is wholly responsible for her actions, the townsfolk—like Emily's father—have acted as enablers, keeping her detached from the rest of society, and thus ensuring that she remains trapped in a dangerous little fantasy world all her own.