About the sideways glances: Nursing in public places has become much easier for me using the First Years’ nursing wrap. It’s like a poncho and it’s the most discrete nursing cover that I have found (it also covers the back, so that it covers you no matter how much your baby kicks and moves around). It comes in beige or black and is easily machine-washable.
http://www.walmart.com/catalog/product.do?product_id=4631187
They also sell it at the Babies R Us in Emeryville.