I was there for a morning run (Princess half marathon) and found that the buses were the way to go as they do close some roads and close them quite early - at least for that race. But that ran between Epcot and MK, I believe ToT run runs between HS and ESPN World of Sports. If so based on what occured for the Princess, the roads between HS and World of Sports would be closed - several hours before the race line up. For Princess (with a 5:45 am start) they started closing roads the night before.
My son and his family stayed at POP and drove to see his sister run, but he lives in FL and goes to Disney 5-6 times a year and knows his way around so he was able to get around the closed roads.
For the Princess, all the resorts were sold out, but there was a lot happening that weekend as the NBA was having their All-Star game and activities and some of the Disney hotels were also host hotels for the All-Star proceedings (I know that Yacht Club was one as that is where we stayed).