I know I'll be downvoted for having an opposing opinion, but I disagree so much. Skyward Sword shines in a lot of areas that no other Zelda has, but... in my opinion, absolutely not in the places you described.

Skyward Sword has one of the best stories in any Zelda game

I'd agree that it's concept and general fullness was better than most, but the execution of most elements was awful. An explanation for the origin of Link, Zelda, Ganondorf and their re-occurrences? Awesome. That explanation essentially being Ganondorf 0.5 saying "cuz I curse you guys". Awful.

The characters are memorable and have great designs

I do agree with this except for two places. Link's face, and Zelda's over-all design. Link's body design was my favorite since OoT. It was properly proportioned, and he finally finally grew some legs that didn't look like they were atrophied... but his face... I don't understand. Why do his lips look eternally irritated? Why does he have bags under his eyes? Why does it look like he's wearing poorly-applied eye-liner?

Then Zelda with her almost-bowlcut, one-tone attire, and general flatness killed me, especially after I saw her original concept art which was miles better.

I was also really turned off by the hyper-anime approach they took with the story, including almost every trope you'd find in shows like Inuyasha or Naruto. I'd have loved it when I was younger, but I just can't fight past the cheesiness anymore.

And lastly it has some of the best music in any Zelda game.

This is where I disagree the most, except for a few songs. Skyloft's theme, to me, is one of the greatest songs in Zelda history. It's got a Joe Hisaishi feel, and that is always fantastic. Bamboo Island is a fantastic throwback, and Tubert's Thrill Digger has a fantastically relaxing vibe. However, almost every other song lacks anything interesting or compelling whatsoever to me. Koji Kondo inspired me to start playing instruments at the age of six, and his unique and interesting music design and technique is completely absent from SS. It's soundtrack isn't necessarily bad, by any means, but to me it's mostly just... generic. Like a typical Hollywood movie orchestra. It just relies on the basic, overly-conventional writing that any other underscore-based soundtrack does. Koji Kondo had an amazing amount of uniqueness, culture, and unusual concepts within his music, and to me that's what makes him stand out as the legendary composer that he is. Without him, the music felt distinctly unlike Zelda, and more-like... well, most other things.

Now where I thought Skyward Sword shined was in things like its overall art-style, and its polished, tight gameplay (despite the motion control hiccups). Upgrading your items was awesome, though it could have been handled in a less 'grindy' way. I too enjoyed the dungeons a lot, especially their atmosphere. The areas, despite being (waaayy too) linear, were designed in a beautiful and interesting way.

Over-all, the reason I'm sour towards Skyward Sword is that it attempted so many cool concepts, and thus had an amazing amount of potential, but fumbled most of it... at least in accordance with what I personally enjoy.