I NIP all the time I never limited when I went out with my baby. To me it's not a big deal. Just feeding my baby. I've always used a big stretchy wrap (I own 3 of them). IMO it's much better than a nursing cover because it's more versatile and you can cover the baby's head or just face or nothing at all. It's helpful if they unlatch quickly so you can cover yourself with the wrap until you clip your nursing tank back up.
This is something like what my wraps look like. I pretty much never left home without one on when my baby was younger.