The sign read WHITE CITY INVESTIGATIONS.
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The detective agency is either new enough to have named itself after the World's Fair or possibly changed its name to take advantage of the association. It might also have opened up merely to solve some of the myriad problems that would inevitably crop up when you bring so many strangers and tourists together in one place.
The detective agency he sought was located in a seedy block of the New Levee district, between a variety saloon and a manufacturer of exploding cigars.
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Pynchon has already made a few references to Star Trek so I can't help reading this set-up as Randolph St. Cosmo on the holodeck searching for Picard's Dixon Hill office.
"New Levee district"
I don't know anything about Chicago in the 1890s but this may have been the Red Light district. It's right there in the description of the building surrounding the thing Randolph is searching for: drink to loosen up one's morals and exploding cigars to represent ejaculating penises.
"a variety saloon"
Unfamiliar with the adjective "variety" before the noun "saloon," I had to look this up. It just means "an evening of mixed plays." So this is like a McMenamins or an Alamo Drafthouse.
