What are some ideas for unique gifts for my Army Brat teenage boys?

I'm in the give them your time category like 1LT (Join to see). Kids are most affected by experiences, not things. Some are family traditions like we took our kids out to the beach house every summer. A week camping trip with dad, some fishing, plinking, beans and bad stories by the fire,... another memory.

Take them on a trip! Just you & the boys.. camping/fishing or snowboarding/skiing, etc. Something unique that they will definitely remember. I imagine that throughout your tenure, you may not have been able to spend a ton of time with them, so this might be something that they would prefer over a material item.

Your sons probably traveled with you during your military career. Our kids move all over, a life we take for granted and for which we have memorabilia. They will grow up with memories, but not the memorabilia. One way to recognize their support (since it is customary to hand family members some token at the ceremony) would be a plaque or other memento which represents all the places they have lived. You know - "To the Son of a Soldier - in recognition of the fact that you also served and sacrificed." or " Joe Whitman - MVP on MAJ Bill Whitman's Support Team" Then list all the places he lived and the dates, maybe with a picture or greeting in the language or local dialect (eg., Guten Tag, Anyong Ha Seyo, Howdy, Good Morning, G'Day...). A nice line thanking them for your support at the end and they will have something they can cherish and display always; it might even mean more later in their lives than immediately.