Each of the area's in Skyward Sword were done pretty well in my opinion, I'd like to talk about the pros and cons of each area and then state which one I felt was the best.
I'll start with Faron. Being the first overworld area in Skyward Sword, Faron Woods sorta gives you your first taste of the game and sorta let's you know what to expect throughout the game. It's a great starting area, it's music is fantastic! Fitting the area perfectly with a mix of excitement and curiosity to it that sets the atmosphere of the Woods perfectly. Being the pretty much the first place Link has been on the surface other then the Sealed Grounds, Faron Woods is sort of where Link has gotten his bearings and is ready to really knuckle down to his quest, so I think the music fits perfectly. Faron Woods has also got to be one of the most visually amazing areas in any video game I've ever played. While that can be said of almost any place in Skyward Sword, the Faron Region nails it better then any of the other areas. As a whole the region looks outstanding. The tone of Faron Woods is incredibly light hearted and they did that well, although it's not my favorite tone of the game, they executed it well imo and I think the Faron area was done very well. It's dungeons are really good too. I liked Skyview Temple, as it's music complimented the dungeon incredibly well and it was a semi challenging first temple, which is refreshing and also managed to have a very good boss fight. The Ancient Cistern was one of the most visually impressive places I've seen in Zelda, and I loved the Dungeon, it wasn't my favorite, and the music was sorta meh, but overall it was a good temple with a epic boss to cap it off.
Eldin. The fiery mountain region, a unique and rugged beauty to the area, it as a whole focuses more on gameplay then it does the whole atmosphere. I found that in that department Eldin is somewhat lacking, but has some of the funnest gameplay in Skyward Sword. The music for Eldin Volcano is good, although I'm not sure it's the best they could've done for it but that being said, I still liked it. The Earth Temple was really fun, despite being one of my least favorite Dungeons in SS, it's steal one of my favorite in Zelda.

The Fire Sanctuary was also incredible, it used to be my favorite in Skyward Sword (aka the series) but that has been taken by a different Temple, it's gameplay was ridiculously fun. As a whole the Eldin Region was good, not great but it was good.
And now we come to Lanayru. Lanayru's region started out incredibly boring to me, and I'd say it has one of the slowest starts to a region out of the Zelda series. That being said once you get off the ground and get to the Lanayru Mining Facility, things really start to pick up. Lanayru as a whole really focuses on the atmosphere but still backs it up with strong and entertaining gameplay. The music to each place in Lanayru fits their places flawlessly, each seeming to have an element of mourning or sadness, which I believe is a big part of Lanayru as it is a scorched and dead land (prior to hitting the timeshift stone) and there seems to be a sadness about the whole area as a result. It's a land that used to flourish and be a place of life and beauty, now it is not even a shadow of what it once was. The music that goes to Lanayru Harbor captures the feeling of sadness perfectly and creates the perfect atmosphere. Every time I play through Lanayru I'm just breath-taken by how well done it is. The dungeons were cool too, Lanayru Mining Facility is probably my least favorite dungeon in the game, but it's still a good dungeon overall, focusing heavily on puzzle based challenges which is cool but doesn't really make for great re-playability value. That being said it's still an awesome ride. Then you have the Sandship, my favorite Dungeon in the Zelda series. I think it really helps that the bow and arrow is introduced to the game in that Dungeon, being my favorite item. The theme to the dungeon I really liked as well, and the gameplay was really good. I especially liked the shootouts with the Bokoblins as easy as they may have been, it was one of the most enjoyable moments in the game for me.
So overall I guess it's obvious my favorite is Lanayru. It just was the strongest in terms of atmosphere and gameplay, it took the best from both of the previous regions and turned it into a incredible region that was pretty much flawless.