Peel hard-cooked eggs and halve lengthwise; carefully use the tip of a spoon to remove yolk from each egg half. Set whites aside. Place yolks in a small bowl; mash with a fork. Add mayonnaise, mustard, and vinegar; mix well. Add bacon, tomato, and basil; mix well. If desired, season to taste with salt and pepper.
Stuff egg white halves with yolk mixture, using a rounded teaspoon of yolk mixture for each half and using the back of a second teaspoon to carefully push the yolk mixture off the first spoon into the cavity of the egg white. (Or place the yolk mixture in a large resealable plastic bag, snip off one corner of the bag, and squeeze bag to pipe some of the yolk mixture into the cavity of each egg white half.) Cover and chill until serving time (up to 24 hours). If desired, top with additional bacon.