Combining the terms "Martial Art" and "avoiding head strikes" is a tall order. The two are mutually exclusive, honestly. The head and its surrounds are excellent and strategic targets in all arts martial. That said, there are plenty of so-called martial arts that reduce their focus on head strikes, primarily for liability reasons, or out of ignorance. Tae Kwon Do includes head strikes, but various schools tend to minimize this aspect of the art.
Each instructor of each art tends to emphasize certain aspects more than others, so I would recommend you attend a training session and talk to the instructor about your concerns and interests.
Perhaps you would do well with a martially inspired exercise regimen - Tai Chi, Tae Bo, or some form of aerobic kickboxing where contact is extremely limited.
Also, some of the sport variants of Tae Kwon Do and Karate have less contact than their martial brethren and might be good to investigate.
Don't expect to find a serious martial art that doesn't include head strikes. Head contact is a whole other consideration. Control is the issue here, practice striking towards the head does not necessitate actually making contact and this is where observing classes is key. Don't go to a school where folks are boxing each other's head and face unless you want to enjoy all that that contact entails. I'm not suggesting there isn't value in making some contact, just that it should be very controlled.