My understanding is that the danger from radar is the heating it can cause (think microwave ovens). The most sensitive part of the body is the eyes.
This said, the average power (and thus heating capacity) that a radar antenna transmits is pretty small. But it is concentrated in the horizontal plane of the antenna. I would not hesitate to balance an antenna on my head, or use it as a pillow. But I would not be comfortable with it at eye level.