Some mothers have good luck nursing in a sling or soft carrier, and it covers everything. My daughter needed to nurse every couple hours, and often more. Sometimes out in public she was happy going longer without nursing, once when she was still tiny we went on a long hike, then a coffee shop, and it was like 5 hours between feeds that time- if there was plenty to see, but not too stimulating. But the opposite was true too, if it was overwhelming or boring or uncomfortable she'd want to nurse more frequently. I realized that if I wanted a life that involved leaving my house and being around people I'd have to nurse in public. I was committed to nursing on demand and tried not to delay feedings. I had a few really good first NIP experiences and then was pretty confident. And no one ever made a single negative comment in any public setting.
The first time I went to a restaurant: I'd been frequenting a small local diner during my pregnancy, I needed PIE! lots of PIE! So they knew me there and were always nice, and seemed to enjoy watching my pregnancy progress. When my sutures healed enough to sit in a restaurant my husband took us to the diner and baby wanted to nurse as soon as we were seated. I expected that because it was an unfamiliar place and there were other people and funny smells. I wasn't very practiced yet but I arranged her and let her latch on, partially covering with a silk scarf, with my husband glancing around to sorta "keep guard" for me, and booths are pretty private anyway, and it wasn't crowded. There must have been a few moments when my breast was fully exposed but no one noticed or if they did, they did not react at all. The host had fawned all over us and ooh-ed and ahh-d over the baby, and when the waitress came to take our order, baby was still nursing. The waitress asked all the questions about when was the baby born, how much did she weigh, etc, and how cute she is, and how glad to see us, and took our order. When she came back with the food, baby was still nursing, she was still all smiles and so nice and arranged my plate and silverware so I could use it while nursing. So far had not mentioned the breastfeeding or acted weird at all, not avoiding looking but not staring either, just acting natural. When she came back to check on us, we'd switched breasts (again with no mishaps even though my boobs must have been visible at some point) and she took away the plates and commented, "wow, she must be hungry!" (we'd been there like 45 minutes nursing the whole time) And then when we paid, she said "my sister is due next month, she's planning to breastfeed too" while she wrung our bill and everything. This first experience went so well- with not one moment of weirdness at all- that I was really reassured. Our waitress was a really nice young woman, but a college girl at a party school, and I felt like if she was cool with it, probably everybody is.
I've had lots of similar moments of mellow, quiet, natural support. We used to stop for lunch at coffee shop every week, and I nursed my daughter there, when she was a toddler. The guy who ran the place would bring out my order (most people get their stuff at the counter) and get my decaf latte started as soon as I walked in the door. He said once, you and your little daughter are always welcome here. And once when I popped out my breast to nurse at story time at the library, the librarian said, "right on", and then another mom began to nurse her baby, too.