So let me start of by saying that my group and I have recently started 5th edition. We are about a two months in and things have gone pretty good so far despite some bumps in the road. My group is really enjoying most of the new mechanics, and the ones we don't we have changed to fit our playstyle. Now I started the group near Baldur's gate where they had a few adventures until they decided to go to Waterdeep a couple sessions ago. They are in Waterdeep and I have come up with a few ideas for quest for them, but need a little help with more since they plan on staying for quite awhile in Waterdeep.
They already cleared out an abandoned Arcane school for one quest, and the other one I have written up is an ancient tomb that has riddles and hints of an ancient warlord that was losing to an unknown enemy. The warlord eventually had a meeting with a man and was turned into a vampire ( the PCs would not know this going in).
Now I have not run to many campaigns anywhere near Waterdeep so if anyone has some ideas for quest in the city it would be much appreciated!
I once bought the 4th edition waterdeep campaign guide. It has a lot of info on the city and a bunch of adventure hooks.
If you want them to stay there for a wile, try a nice murder mystery that continues for a couple of sessions. And don't forget that the (main) access to the underdark can be found in waterdeep!
Infiltration of a guild like the thieves guild or assassins guild comes to mind. Just as a pirate invasion to it's ports.
Or how about a nice zombie apocolypse! everyone knows the movies where the living dead shamble there ways onto the streets...
Look up the Yawning Portal and Undermountain; if your players are into going on adventures into dungeon terrain, Undermountain can provide an actual lifetime-worth of gameplay with is many, varied, and extensive layers and the ways in which they connect to other places (both in and outside of Faerun).
Those are both really good ideas thank a lot. Is there by chance a list of the guilds in Waterdeep or no?
Here's a good resource: The Forgotten Realms Wiki.
3e City of Splendors: Waterdeep sourcebook offers a detailed look at the city. The guilds are listed in there. Undermountain is a book of its own.
The city got a multi-page writeup in the 4e Forgotten Realms Campaign Setting, with a lot of material that you have to skim 3e FRCS to 'get' the update.
If you are tying in Tyranny of Dragons somehow, the City has defences that make it a fairly safe place to stay. Refugees will stream here in droves.
A military supply base will naturally be built eventually, too; it's the biggest commerical port on the Sword Coast.