Thanksgiving is the busiest holiday in America. So you can definitely expect everyone to be on the road on the 21st (Wednesday before Thanksgiving) and on the 25th (Sunday after when everyone will be heading back).

Unless you have already successfully booked your tickets in advance or will be braving the traffic jams, the best you can do is to avoid the peak days.

Note that...

The peak travel days are: 22 Nov (Wednesday before Thanksgiving), 24 and 25 Nov (weekend after Thanksgiving).

The best days to travel are: 17 (Saturday before Thanksgiving, way before the crowd starts traveling), 23 (day after Thanksgiving) and 26/27 (weekday after everyone else has gone home).

Not only will you be able to avoid the crowd if you travel during these days but you will also be spared from paying a ridiculous amount for your ticket, should you choose to fly or travel by train.