The general rule for bullet points is consistency:
Punctuate bullets consistently. That is, if one bullet ends with a
period (full stop), end all with a period, following these rules:
a. If all bullets are sentences, end each one with a period (full
stop).
b. If all bullets are phrases or fragments, use no end punctuation.
See more at:
http://www.businesswritingblog.com/business_writing/2005/12/the_best_of_bul.html#sthash.7LoRdiUR.dpuf
Your bullets are not employing full sentences, so the periods should probably be deleted:
- Creative Campaign Themes: “A Beach with an Accent” and “Come Make Memories”
- Brand Position (what we want to be known for): Unique combination of the sophistication of the traditional South with the serenity of a
beach vacation; One of America’s top 10 island destinations
Because your points have sub-points, you might consider a further improvement:
Creative Campaign Themes:
a. “A Beach with an Accent”
b. “Come Make Memories”
Brand Position (what we want to be known for):
a. Unique combination of the sophistication of the traditional South
with the serenity of a beach vacation
b. One of America’s top 10 island destinations
And since sub point 2 a. is a combination, you might even consider:
Creative Campaign Themes:
a. “A Beach with an Accent”
b. “Come Make Memories”
Brand Position (what we want to be known for):
a. Sophistication of the traditional South
b. Serenity of a beach vacation
c. One of America’s top 10 island destinations
The colon of point 2 belongs to Brand Position, so you would want to place it outside of the parenthetical phrase (what we want to be known for).