I'd imagine just finding a place to breastfeed in peace and privacy would be hard if you go somewhere new and a place you're not necessary familiar with. I know some moms who can't seem to breastfeed because they are too self conscious in public, even in nursing rooms -- they call it performance anxiety of sorts. So they either go out for short periods of time, at nearby places and head home to feed baby or don't take baby with them if they need to be out and about for too long.
For me, the biggest challenge was to find a nursing room. My hub was not comfortable for me to bf my children in public, using nursing cover. He felt others are looking at us. At times, one of the challenges is having to wait to use the nursing room. N it can take a while as others are also bf their LO. Hence, we usually prefer to go to bigger malls with bigger n more nursing rooms