I feel comfortable making the claim that so far, The Legend of Korra is the greatest children's show ever to exist, and one of the greatest shows overall.
Let's go down the list: first, the animation is gorgeous, and that's one of the first things I noticed. The voice acting, the sound design, all of it is perfect or near-perfect. In regards to the technical stuff, The Legend of Korra should be used as a standard for other animated shows to reach.
The character design is extraordinarily well done. Korra makes a very interesting protagonist. At first, she appears to be another shonen-esque, headstrong, fiery character. However, she is shown to be more nuanced than that: she is clearly inexperienced and a bit nervous in regards to romance, and she comes to fear the villain, Amon, creating an inner conflict between her duties (and her outward eagerness to take Amon down) and her secret fear of Amon. I can hardly blame her for that fear: Amon, while not very different from the menacing villains of other shows, is extremely adept at being menacing, and makes a great villain. Furthermore, when we learn his backstory late in the season, there's an ever-so-slight hint of good in him, which helps humanize him while failing to make him any less threatening. The other characters, too, are nuanced and well-written, but none of them are as interesting as Korra or Amon, and so I won't lengthen this paragraph any further by delving into any of them.
The setting is extremely interesting. I was initially uncertain of how the new setting would change things, but it proved to be even more interesting than The Last Airbender's feudal world (although YMMV). The urban setting and steampunk gadgetry lend themselves well to the new characters and conflict. I can only hope that the next season will explore Republic City in more depth.
The plot is mesmerizing and fast-paced. It is very well-written, with a few interesting twists. Notably, it explores more mature themes than most children's shows. You find yourself itching to watch the next episode, to find out what will happen next, in a way that few shows manage to elicit. I won't go into detail: watch it yourself, and enjoy each new discovery.
Finally, the romantic subplots and action scenes are handled well, and were very enjoyable. Overall, I would recommend The Legend of Korra to anyone wholeheartedly.