Ok, I'm going to start off saying that women should nurse in public wearing or not wearing whatever they want. Some women feel comfortable just lifting or unbuttoning their shirt. Others prefer to cover up with a blanket or other accessory. It's all good.
Personally, I don't like using a blanket or cover when Jo is nursing in public. Jo doesn't like it either. I try to wear things that are easy to shift around for easy access, and I feel more comfortable with a little coverage over my chest (but not covering Jo's head). So scarves are perfect for us. Especially extra long scarves. I just wrap it around and around and around my neck and it drapes quite nicely during nursing. I tend to wear a scarf often anyway so I don't even have to put anything additional on.
I also really love Jo's little UB2 bonnet as a nursing accessory. The brim is super wide so it can hide a bit of my chest while Jo's face is still uncovered. It covers the side-boob thing too so I don't always have to lean one way or the other as Jo latches on. Plus it's super cute!