Royal Oaks, Michigan
So we learn in "Driving Miss Hazy" that the Loud family lives in Royal Oaks, Michigan (it's printed on a driver's license)
As far as I know, The Loud House is only the second Nicktoon to be set in a specific state after Rugrats was set in California (the episode where Lou takes the kids to the museum has a close-up of Lou's IMOLD California license plate)