3. New York Yankees
The Chicago White Sox should not give Dylan Cease to the New York Yankees.
The New York Yankees are one of those teams that is in the mix for every player via trade or free agency when they become available. They don't get them all but they are always competitive with their offers.
It would not be fun to see Cease as the next one in that long line. Just like the other places, New York is a team that would probably see him become a star. Nobody wants to see their players go to the Yankees and dominate with them.
The Yankees aren't in the AL Central so they'd play against Cease a little less than if he were traded to a rival but they still play enough for it to be annoying too.
Instead, it would just be better to see the White Sox move their prized trade asset to a team that they won't face all that often. A nice NL team would do the trick.
Seeing him on one of these teams would be so frustrating. It is already bad enough that the Sox are in a position that they have to deal him so that would make it even worse. Hopefully, regardless of where, the Sox get a good return.