With Jan 1 being on a Saturday, I would say most people's vacations will probably wrap up on Sunday the 2nd.
I would avoid around the Dr. Martin Luther King weekend. It is a great long weekend for many. Additionally, most of the schools in our area (NC) end their fall semester the week leading up to MLK. By us, the Friday before is a finals make up day, so many of the older kids really have that day off. And since they do finals in the morning here, it means people like us can be on the road by noon on Thursday.
Further, the Tuesday after MLK is a teacher workday (basically for them to finish grading the finals). In some school districts, so is Wednesday. So many people turn it into a four, five or six day weekend.
Two other points. I think RunDisney does one of their runs the second weekend in January. Not sure if those have restarted or not (I am not a runner). The Disney Skyliner between Caribbean Beach Resort, Riviera Resort, and Epcot will be closed for refurbishment from January 23, 2022 to January 28, 2022. These may or may not impact your plans...
Other than those weekends to watch out for, I think you are safe any time the rest of the month.