In most of the South, slavery had already been abolished before the Thirteenth Amendment. The Emancipation Proclamation on January 1, 1863, freed all slaves in (essentially) all territory still Confederate-occupied; the Union Army then enforced abolition as it marched through each plantation. As you can see, most of the exceptions were either border states or close to Union-occupied cities like Washington, Norfolk, and New Orleans where the news of abolition - when it happened - would quickly reach freedmen.

However, sadly, some slaveowners did manage to conceal from their slaves both the Emancipation Proclamation and the Thirteenth Amendment. Bruce Levine's Fall of the House of Dixie mentions incidents where this happened in both Texas and Georgia, and I'm sure those weren't the only ones. Most just tried to pretend nothing had happened, but one master who tried to explain it by claiming Lincoln's death had restored slavery. One African Methodist Episcopal missionary in Georgia said, even four months after Appomattox, "The people do not really know that they are free." This did eventually fail, one plantation at a time, without much fanfare. Levine quotes one newly-freed girl saying that "another year after freedom... we finally found out we were free and left" the plantation. Sadly, though Levine doesn't speculate, it's unlikely she was the last to learn.

There is u/MrDowntown ‘s comment here on the importance of Juneteenth and how celebrating it among African American people spread outward from Texas that addresses Texas slave owners ignoring the 13th amendment. u/cake_flattener1 also has a good comment further down the thread. I don’t know of others, but Juneteenth is perhaps the most prominent.