Erelhei-Cinlu is on Oerth
There is no officially published conversion to 5e from WotC for the D-Series modules, but for several other modules 5e has issued recommendations on relocating things from other game worlds to the Forgotten Realms.
Most relevant here are the "Against the Giants" modules (G1-G3, G-Series) re-published in Tales from the Yawning Portal. These adventures like the D-Series with the city of Erelhei-Cinlu you are interested in all originated in Gary Gygax' home Greyhawk campaign, the original campaign the led to the publication of Greyhawk as a setting. The D-series continued the storyline of the G-Series, and the intro to D3 (p. 2) states:
As a member of a bold party of adventurers, you and your associates have trekked far into what seems to be a whole underworld of subterranean tunnels—arteries connecting
endless caves and caverns which honeycomb the foundations of the lands beneath the sun. From the entrance to this maze found on the lowest level of the HALL OF THE FIRE GIANT KING (DUNGEON MODULE G1-2-3), your expedition has dogged the heels of the Dark Elves
So if you locate the Hall of the Fire Giant King, you know the entry point to the underdark for the D-series. Based on the guidance from Tales for the Forgotten Realms the location of the Hall is one of these:
In Faerun, the giants could be raiding the Sword Coast after emerging from the Sword Mountains or the Sunset Mountains or the Spine of the World.
They might be preparing to move on Damara from out of
the Galena Mountains, or to descend upon the Dalelands
and Cormyr from the Stormhorns or the Thunder Peaks.
Either of those would be a recommended starting point for the underdark hex map provided in the D-series modules. This hex map shows the location of Erelhei-Cinlu relative to that entrance point. As the overall extension of that map is only about 50-60 miles, it would be pretty local to whatever mountain range you choose, compared to the size of the Sword Coast map that covers over 1,500 miles.
The adventure locations are introduced like this in Tales:
PLACING THE ADVENTURES
The preferred habitats of hill giants, frost giants, and
fire giants exist in virtually every D&D setting, so it's not too difficult to find locations
Both from this and the flexibility of suggestions where you could place it, it seems all you really need is a mountain range with human lands to be raided nearby for your starting point, and you should be fine to put it whereever it makes sense for you.
A major drow city in Fearun would be Menzoberranzan, which is described in the module Out of the Abyss, along with a description of the Fearunian underdark at large, which may be of use.
One piece of advice I have is that the D-series is targeted originally at character levels 9 and up. If you come straight from Wave Echo Cave, as your party should be at best level 5 after Mines of Phandelver, you'll have to bridge the gap up to there if you want to convert to the levels.