With my first baby, I was extremely shy about breastfeeding and didn't want ANYONE other than DH around me when I was feeding DS. When I was out in public, I initially hid myself in bathrooms and as DS got older I just started carrying bottles of formula around with me (I wasn't able to pump enough). This resulted in me often missing feeds and from an early age my supply dwindled and although I was able to bf until DS was 8 months old, he had to be combi-fed almost the entire time. As other OP's have said, I felt extremely isolated. Whenever we had friends over I went upstairs and hid in our bedroom, but DS was a SLOW feeder and each feed took 30 - 45 minutes so I missed out on loads of social time and felt really withdrawn. I was also upset with the amount of well-meaning people who told me that I *shouldn't* be bf'ing in the bathroom, and that I should be able to do so where ever I wanted, because I just wasn't comfortable with that.
When my DD was born, I did a complete 180. As others have said, I 1) didn't have the time to hide in a private place while my DS was running around also, and 2) I felt a lot more confident with my ability to bf (and DD was a champion nurser!) so I bf'd anywhere and everywhere. I used a cover exactly twice, and it was extremely uncomfortable and I couldn't see DD well and it irritated her. I also started baby wearing and learned how to use my stretchy wrap to help feed DD one-handed (and also help cover/hide her) and I always used the 2-shirt approach (one up, one down) so there was very minimal exposure.
Ironically, the only one who EVER made any comments about my breastfeeding in public was my own mother (who pretty much thinks it's inappropriate to bf in public at all) but we live in different countries so this was only on a few occasions when we were visiting. DD was bf until 16 months and I did feel uncomfortable NIP'ing as she got older than 9 / 10 months, but before that I never had any issues.
In general, my opinion about breastfeeding in public is that it shouldn't be an issue. I think it's respectful of others to try and do so discretely, whether for you that's using a cover, or the double-shirt approach, or whatever else works for you. I still feel a bit uncomfortable when I see others bf'ing in public (which makes no sense at all, I know) but I always applaud those mothers in my mind for being able to do so. I don't think it's unreasonable that some parents don't want their own children exposed to "blatant" (entire top down?) nudity while breastfeeding (not all parents are prepared to answer the questions that might follow from their own children, and I can respect that also). With all the other terrible things going on in public places, I don't understand why people pick something as natural as breastfeeding to get upset about...