In the case of Innsmouth, you have a pretty easy setup to work with (minor spoilers for "The Shadow Over Innsmouth"):
So, in the case of Innsmouth, you have a few interesting "business" possibilities:
- Up through the 1830s, the Innsmouth fishing fleet isn't catching very much. These ships might better be used for other, less savory purposes.
- In the 1840s, the Marsh family has come upon a mysterious supply of refined gold which he has been privately (and suspiciously) smelting down into ingots before turning it into proper money. The source, location, and control of this gold would all be of interest to blackmailers, smugglers, embezzlers, and racketeers of all sorts.
- In 1846, something goes really, badly wrong in Innsmouth, resulting in a shift in the town's balance of power, while the "epidemic" there leaves a power vacuum, and the fishing dries back up again. Once again, Innsmouth looks like a place of opportunity for anyone in need of a ships and people who aren't inclined to talk about what the ships are used to import or export.
- In the 1870s, the gold tiara smuggled out of Innsmouth might reawaken the interest of adventurers and opportunists.
- In the 1920s, Prohibition would awaken a market for illegal alcohol imported from Canada; heavily publicized international incidents involving such illegal imports, sometimes arranged between Canada and state government officials in secret, would challenge federal authority, and would begin making a quiet port town with a mostly forgotten fishing fleet capable of quietly importing Canadian whiskey would start looking really attractive.
- Through the raid over the winter of 1927-1928, there will probably be a lot of people in Innsmouth with a lot to hide who would be willing to pay dearly for quiet and quick transportation out of Innsmouth; someone capable of bribing or extorting cooperation from officials enough to allow key figures from Innsmouth to escape the raid could quickly line their pockets with alien gold.
- After the raid ends in 1928, control of Innsmouth is left once again in doubt, allowing great opportunity for the right (or wrong) sorts of people to step in and take advantage of the lawlessness, disorder, and confusion. There might even be caches of military weapons and ammunition, leftover stashes of Marsh gold, and other treasures to loot from the town.
I'll have to refresh my memory on opportunities in Collinsport, but the history of Collinsport is similar in many ways to Innsmouth, minus the whole Deep One and Innsmouth Raid affair, and the opportunities are similar. One of Collinsport's big running Mythos gimmicks would be vampires: several members of the Collins family were vampires, and Collinsport is only a short distance away from the location of Stephen King's Jerusalem's Lot ('Salem's Lot). You might get a lot of mileage from a criminal gang that makes a deal with the vampires, helping to transplant vampires from Collinsport and Salem's Lot to other locations in "Lovecraft Country", for example, or importing a steady supply of victims for the vampires to feed from. The cult of the Leviathans might work with gangsters in order to retrieve artifacts such as "Naga Boxes" (containing gateways between the Leviathans' prison and our world) from private collections and prisons. Criminal gangs might move into Collinsport for any of the usual reasons (drugs, prostitution, gambling, racketeering, money laundering, etc.), only to find that the cult of Leviathan and the Collins family already behave like criminal organizations, leading to uneasy truces, or open warfare, or both. Collinsport runs a successful cannery, a struggling fishing fleet, corrupt and backwards local government, and any number of local businesses that might be exploited for "protection" and other rackets. Deep Ones, Deep One hybrids and collaborators, and other shady characters fleeing from Innsmouth might think Collinsport looks like the next best thing to Innsmouth, and might pay organized criminals to help smuggle their way out of Innsmouth and into Collinsport....
If you want landed (if down on their luck) "aristocracy" try some of the coastal towns of the southeastern USA, especially the Gulf Coast from Tampa around to Galveston. Louisiana and Mississippi add voodoo into the mix and the whole region can contribute the KKK to the background. Tampa and New Orleans are firmly mob-controlled (as BTW is Providence RI), but there are lots of homegrown rum runners and bootleggers.
Oh, I like the sound of Gaffer's suggestion here. Check out Season 1 of the TV Series "True Detective" for pulp detective/horror story set in the Southeastern USA, mixing organized crime, small-town corruption, and voodoo with the King in Yellow mythos.... Just brush up on your Southern Gothic tropes (link) and invent a small southern town full of shady characters to corrupt, and you're most of the way there!