Shinsekai Yori really surprised me by developing some pretty heavy themes throughout the last two seasons. If you're a sci-fi fan, read on.
Story: Set in a utopian/dystopian future (depending which species you belong to, I suppose), it is about a girl named Saki growing up, being confronted with problems of her society's own creation, and then piecing together the truth of her people's history while solving the various issues that crop up. The issues start small and ramp up, and the foreshadowing and doomsy, creepy vibe seeps into every nook and cranny of the story as it progresses.
The storyline is notably complex--which I actually thought was its main downfall. The first few episodes lacked what I like to call "signs of a coherent narrative" (ie a clear objective for the main character) and I very nearly dropped it around episode 4. That's my biggest criticism though, and if you stick with it long enough for the plot pieces to start falling into place, it's very rewarding.
Animation & Sound: I have no complaints here, but then, I favor pretty art over gritty art. I did think, though, that making everything pretty enhanced the sense of utopian peace love and happiness--so that when the darker parts came out, it enhanced the sense that they'd really tried to sweep all forms of badness under the rug and failed. Music was great.
Characters: I thought they were a little weak. Saki isn't overly complex, just your basic do-gooder. Nothing that happens to her is actually of her own personal making, which weakens her development. None of the other characters were particularly remarkable, but they weren't bad either. Just kind of average.
In the end, Shinsekai Yori is not for anyone with a short attention span. It offers some very heavy themes, almost hard to watch at times, and doesn't shy away from any topic. It is a very thought-provoking watch, and well worth your time.