My first daughter nursed in the football hold exclusively, and so far my second daughter is the same. I have large breasts which make the cradle hold impossible or at least unrealistic. :P
I carry a large, overstuffed diaper bag or purse that I combine with a wadded-up sling to make a pillow. If I can't find a chair with arms, I will try to: wedge myself next to a wall; if sitting in a booth, turn sideways to use the back of the booth as a wall; if in a straight-backed chair, turn the chair (or myself) sideways so I can wedge my improvised pillow against the chair back. . . . Once we're positioned, I tug my shirt down to obscure my nipple.
In terms of being in public, I think it helps to NOT gaze adoringly into my baby's face, but instead to talk with whomever else I'm with. I think people catch on to the fact that a baby in a cradle hold is probably nursing. Some folks can't figure out what the hell I'm doing with the football hold until they've stared long enough to get an accidental eyeful.
I hope this helps! Good luck.