
Mikhail |

City of the Spider Queen
My group played in CotSQ few years ago, but it's edition 3.0 I think.

Rotolutundro |

There's the Throne of Night series coming out. I seem to recall some adventure about helping dwarves (something about herding beetles?) by delving into the Underdark, possibly in Dungeon, but I'm afraid I can't remember it's name. It wasn't The Chasm Bridge in 101, or Zenith Trajectory in 102 or Sinkhole in 103... but as you can see, there ARE adventures set in the Underdark (or at least, underground). I hope you find one you like.

LizardMage |

You could probably adapt the Second Darkness AP to Faerun. It's extra work,, but I think it would hit what you're looking for.
EDIT: so after posting I went and re-read it, as I have considered ordering it recently, and it might not be the best. It does have a book where you travel to their drow city for an adventure, but the others are various other travels. Your call it might be something that interests you.