If acquired earlier on in the game, the bandana can be used as rather effective headgear and even combined with eye wear (like sunglasses) to offer slightly more DR. The +1 bonus to Perception can also help characters spot enemies from a further distance.
The bandana will also never deteriorate. Once at 100%, it remains at 100% condition throughout the entire game no matter how long you wear it.
Bandanas are rare in the Capital Wasteland. The plain bandana can be found on Ryan Brigg in the Jury Street Metro Station, from Robert of The Family in Meresti station, and randomly from the generic Megaton settlers in Megaton. The unique red variant can be found, appropriately, on Red, which can be taken from her without force during the quest Big Trouble in Big Town, or when enslaving her in Strictly Business.