Hover the mouse over the Neighbor you would like to hide and click the Hide button.

A message will pop up to confirm the action,
To re-add a hidden Neighbor, click on the “Add Friends” button and then the Hidden Friends tab.
Each hidden Neighbor is removed from your Neighbor Bar and your Neighbor Count reduces by 1.  Neighbors who’s been hidden aren’t affected by you hiding them. They can still visit you and your profile picture will be there on their Neighbor Bar.  Also, unhiding can only happen when the player is under the limit of 300 Neighbors.