It actually makes me very happy to see women breastfeeding in public. I'm glad more and more people are doing it. It's absolutely nothing to be ashamed of and I'd love to see it become the norm.
As for using a cover, I did for a few months until my LO started kicking it off and refusing to nurse under it. I won't bother for the next one. I honestly think a cover can draw even MORE attention to what you're doing than just feeding without one. You can feed discreetly without a cover. It takes some practice, but can definitely be done. The two tops (one pulled down, one pulled up) works very well and shows very little.
As for finding separate rooms to nurse in, well, I did that for a while, too. Until I ended up spending most of my time segregated from the people I was trying to spend time with.
Honestly, I can understand why someone might be slightly uncomfortable by not knowing where to avert their eyes or something, but if someone is so uncomfortable with it that they think a woman should hide away to feed their child, then I think they need to grow up.