You've got some really interesting thoughts! Here's some of mine; as I'm likely to recycle the (really nicely done) PotA dungeons anyway, it helps to hash out my likely options.
Actually, I think most of the surface dungeons do fit into the urban environment. Feathergale Spire can be plunked down at the base of Mount Waterdeep or in any upscale quarter.
I think that Feathergale makes the least sense in Waterdeep, simply because it clashes too much with the Griffon Cavalry on a conceptual basis. I'd want to keep it out of the city just to avoid player confusion! That said, there is a perfect place for it: the
House of Stone. Just change up some of the descriptions and it should work, and it's really not far from the city. Either way, I'd keep the Spire out of the city, so that it's 'hunting lodge for bored nobles' theme can work, and to avoid awkward issues like "Why don't the Griffon Cavalry watch these guys?"
Rivergard Keep can be placed in the harbor.
Probably makes more sense for a pirate hold to be out of the city, like Roaringshore is to the south. I actually found Rivergard Keep quite boring in play though, so it's really no big loss to just quietly ignore it. Dropping it, and putting the Temple of the Crushing Wave (level 7) into the sewers would probably be fine.
The monastery could be...a monastery--Waterdeep abounds with religious institutions. (Although I would probably reskin it as the estate of a reclusive noble. There are no shortage of reclusive nobles in Waterdeep.)
I do like the idea of the monastery being located in the Sea Ward, with an impeccably respectable exterior and a monastic butler who is the height of well-mannered obstruction. Nothing about the monastery's interior excludes it from being placed in a city, if I recall correctly; and the dungeon downstairs can easily be said to connect to Undermountain, making it a valuable chain in the player's route down.
As for the fire cult...it's probably my least favorite surface dungeon, so I would trash it and start from scratch. A foundry or the like is an obvious starting point.
I actually found this one quite fun, myself; it's a short and fairly memorable episode. The players still, to this day, regard Druids as flighty thanks to the rather gullible ones they met there. But since it's short, replacing it isn't a big deal, and it certainly doesn't match Waterdeep that well, unless you moved it to, say, Amphail and turn it into a parody of that recent failed festival thing that was on the news. A more odd-ball option is the
Rat Hills to the south of the city; the metaplot introduced in the 2e City of Splendours included half of it burning down suddenly, which you could easily retrofit into the activities of the cult. Perhaps they started a massive conflagration and then build a shrine amongst the perpetual flames?
Once you get down to the second level - the Dwarven City stuff - I think it's very easy to handle. Just place it all into Undermountain, which incorporates Dwarven ruins anyway, and change the descriptions on the fly to suit them being of a different character from Besilmer.
Waterdeep is a relatively orderly city, yet there's a deep strain of mayhem lurking just below the surface. Placing PotA in Waterdeep doesn't contradict the nature of the city but rather highlights it.
I certainly don't disagree! I think that your main concern in a PotA Waterdeep campaign would be to try and integrate the bad guys with the Waterdeep rogue's gallery a little; having people like Maaril the Dragonmage seen leaving the Monastery might go a long way into making it feel like a coherent whole. With the city already having a harbour (and a recently temple to Umberlee) you can easily bring in a water theme, while setting the story in winter means that howling gales and driving rain can bring the theme of air into play. Stone comes from Undermountain. The only really tough one is fire, and maybe the Rat Hills thing I mentioned above can help there. With the city working well in an elemental theme, and Undermountain covering all kinds of sins of dungeon placement, it should actually be relatively straightforward to do.
Other fun parts of the modules should be equally usable. I used the Death House from
Curse of Strahd to transport a group from the Trade Ward to Barovia already - no reason I couldn't use it again but without the Barovia! The Doomvault from
Tales can be chopped up into loads of tiny Undermountain pieces, great for "you stumble upon a doorway that leads into a new section...". Parts of
Out of the Abyss can be used if the players in your game go to Skullport and fancy exploring further - just move stuff arbitrarily closer and don't show the players the Underdark map.
Rise of Tiamat has some really cool locations - the Tomb of Diderius, Xonthal's Tower - which are not so far from Waterdeep that you couldn't just use them as free-standing adventures in their own right. Transporting them to the city is a little harder, but Xonthal's Tower is arguably a perfect stand-in for the inside of
Ahghairon's Tower, and Diderius' Tomb could maybe, with enough work, be put into the City of the Dead...