I suspect the reference to "Blackstaff" in the question is referring to the Waterdeep's Force Grey (and the Gray Hands feeding into it), which is run by The Blackstaff. Blackstaff is both the title given to the head wizard of Waterdeep, and the special staff she wields. Her job appears to be to handle threats to the city that aren't military, but are beyond the capabilities of the regular Town Guard, and she runs a "private security force" for this purpose. That's Force Grey. Sort of like a private SWAT team.
They aren't specifically good-aligned, or wizard-centered, but she's a Wizard herself, and runs Force Grey out of Blackstaff Tower, which doubles as a Wizard academy.
As far as answering the question goes, I'd second Roflo's comment on the question about the Harpers. They are good-aligned, but prefer to operate covertly rather than overtly, and are all about the acquisition of knowledge. Basically, spies for Good.
Because of that there's only a very narrow band of folks who they are apt to recruit: Good-aligned characters of Int/Cha based classes, like Wizards and Bards. You're in their sweet spot, and its a really tiny sweet spot, so why not look there?