A while ago, I went on a road trip with my family to the Mall of America. Out of convenience, I did not bring any bottles, frozen milk, or even my breast pump. I would be with my son, and could nurse him myself - I didn't need the extra bulk or worry of forgetting something. I did put my Triforce nursing cover in the diaper bag, however, since I didn't know the ins and outs of Minnesota law regarding breastfeeding. Using the cover, I nursed him in the mall several times throughout the weekend. He's a terribly patient child, crying his distinctive 'hungry cry' while in the stroller, then quieting when I picked him up and staying quiet until I could find a place to sit and get him in position.
If you don't know, there is a Nickelodeon theme park in the middle of the mall. I did use the nursing cover, but it was still quite obvious what I was doing, and to be honest, it doesn't hide much. When I nursed Ganon in the theme park area, the only looks I got were from curious children. It seemed that my fellow parents just understood. But when I was nursing him in the clothing wing of the mall, the dirty looks abounded. Only one look was from someone who had a child with them, the rest were from lone women or groups of women.
Shortly before we were leaving the mall, I was quite warm from all the walking, and Ganon kept pulling the nursing cover aside (he was overly warm as well). With a shrug, I pulled it off entirely and put it back in the diaper bag. I was on a bench in the hallway, and my mother had a comically shocked look on her face when she walked out of the store and saw me there, nursing uncovered! I very nearly laughed out loud - but it would have startled the baby.
Now, if you think about it, a baby nursing doesn't show much breast. My shirt covers the top part of my breast, my bra covers the bottom and outer side, and the nipple is in the baby's mouth. His head covers even more, but you could conceivably look around it from certain angles. The only thing even possibly visible is my cleavage, which my mother, once upon a time, encouraged me to show more of. (Ooh, dangling participle! There will be more of these.)
What people don't seem to think about is that breastfeeding is what breasts were made for! Breasts are not 'dirty' or 'indecent'. All mammals have them, and their sole purpose is to nourish the young. While large breasts do attract mates, that is hardwired because of the reproductive implication that a large-breasted woman would be better able to feed offspring. (Not true, just as it's not true that a wide-hipped woman is better at bearing children, but it still causes a physical pleasure response.) So whip out those ta-tas and feed your tots! :D