For in-depth information on each area check out the specific pages dedicated to each area. These are in the rough order I encountered them first.
Dirtmouth
The first main area you encounter, and will revisit often. It contains a few shops, and the Grimm Troupe once you unlock the DLC.
More Dirtmouth Information >>
Greenpath
Here you meet Hornet for the first time and get Moth Wing Cloak, which gives you the dash ability.
More Greenpath Information >>
Crystal Peaks
You can encounter this fairly early in the game, but you can’t do anything here until you purchase the Lumafly Lantern or get the Desolate Dive spell.
More Crystal Peaks Information >>