I nursed all three of my boys and did so in public many times.    I always carried a large baby blanket along with wearing nursing-friendly clothing whenever we went out in public.  Nursing allowed me to fly in peace with a 3 month old who wouldn't take bottles or a pacifier (for our nursing-friendly GC'ers, he was a comfort nurser!  Yikes!  Kudos to Mrs. DeltAlum for her work, I'd have died without my consultant!)
The only time anyone anyone ever lifted an eye to me was in a mall one day (and trust me, I was paranoid about nursing in public!)  I was sitting on a bench in a quiet and secluded part of the mall, with both my jacket on and the blanket to cover me and baby, and he'd been nursing for about 5 minutes already.  Then this older lady walked over to me and in a loud voice announced something to the effect of "I think it's wonderful what you are doing for your baby."  I was sitting there afraid she was coming to yell at me!  
Seriously though, folks, modesty is key when breastfeeding.  Bathrooms are NOT the place to nurse, unless they have a separate sitting area from the facilities.  Trust me, modest nursing is much better than a screaming parent and leaky mom