I would agree that the square block around the resort is easy and safe, I would run it alone. You can either go left out of GC, left on Katella, left of Harbour, Left on Ball, Left on Disneyland Dr, or reverse that. I would not personally venture out into the neighborhoods around the resort alone, and I would avoid crossing major streets in the early AM, rush hour times as people drive like maniacs around there.
They will not allow you to run in Dowtown Disney, within the hotel property areas, or in the parks or parking lots. I have done RunDisney runs before though and it is SO so fun to run through both parks and backstage!!