Nothing unique or original, but my favorite level still is, and will continuously remain, the Outer Wall.
This level, along with Balcony has the most 'surreal' feel of any of the levels in the game, which really adds to the overall atmosphere
Granted, this map is by no means challenging or blood-pumping, but in the contrast they provide a very calm and reliving interlude right after really an intense, frantic segment, and give the player some time to think over what they've just accomplished, or what they've seen; it's a level that personally made me stop, stand and just take in the beauty of the location, which is something few other maps in Cave Story have even come close to accomplishing.
The second you step out of that door, the whole scene just hits you, all at once. The subtle tragedy but simultaneous beauty and energy of Moonsong really just had me stop there, right at the door, not even moving forward to talk to Kazuma. Almost everything that directly preceded that moment was pretty much downhill for both Quote and the player. Two (or four, depending on which ending you take) pretty major characters have died by that point, and there's been little time for recollection in between the frantic action of the Labyrinth and the unsettling nature of Mimiga Village. Being able to stop, listen, and think about everything that's happened to you at that point brings in so great of an emotional factor that I honestly can't describe, and I'm kinda hoping I'm not the only one that felt it, otherwise this whole post would make me come across as some melodramatic over analyst.
The design of the level, in particular the platforming, can come across as annoying at times, but it's fairly basic and not particularly demanding.
Little changes in physics like the items and certain enemies gravitating toward the wall not only create a minor, but intriguing gameplay change, but help add to the atmosphere and surrealism of the whole place.
Everything just fits. The background, enemies, level design, and aesthetic all compliment each other to create something beautiful, and that's why it's still my favorite after my first playthrough back in '11.