I 100% second Mad God's Key. I've run it twice now, as an alternative intro to a much longer Age of Worms campaign, but that's not the point. The point is that my players found it a great adventure, with lots of variety, both in its original 3.5 version, and also when I converted it to 5e rules (which wasn't overly hard).
It starts in Greyhawk City, covers urban investigations, a chase, and a couple of smallish 'lairs' both in the city as well as in the Cairn Hills. It's for levels 1-3, but in 5e you could probably go with levels 1-4 (maybe completing it levels them to 4). There are no pirates, but hey, there's lots of cool stuff as far as adventures for level 1 PC's go (and not a single goblin, or even a kobold, IIRC).
Kick it off by making sure your players understand they must create characters that are inclined to help others, and you should be good to go. If you want some other advise, opinion etc, there's bound to be a few old posts on the Paizo forums (I'm probably the author of a couple there).
There is even a sequel, somewhat different but equally as cool especially as it's more 'urban investigation' with a fairly realistic plot that progresses regardless of what the PC's do rather than waits for the PC's to arrive. However I'm not sure if that's available these days, as it was published in the old Living Greyhawk thing, which unfortunately was a closed shop.