This topic has already been discussed a lot here in the CR, for anyone that wants to bother finding the threads.
A few points I need to add to this discussion:
I don’t know the source, so feel free to chime in, but halachikally, a woman’s breast when nursing is compared to a hand feeding her child. The tznius issue involved is if she exposes other parts of her chest or her shoulders. Again, please help me out with a source.
Allowing women in the US to nurse in public, since most women are actually uncomfortable with it, is not liberalism. Instead, liberal women should be demanding that malls and other public spaces offer them a safe, women only place to breastfeed such as a women’s lounge. If it’s perfectly legal and okay to do so publicly, why should businesses or government institutions bother accommodating women in this regard? That’s not to say law enforcement should start arresting women that do otherwise, just ignore it if she’s discreet about it, or politely ask her to cover up if she’s not. The issue shouldn’t be breastfeeding per se, which may be a necessity, but exposure.
Back to Halacha, it is assur to nurse a baby in an actual restroom, just as you may not eat in a bathroom. Perhaps in extenuating circumstances exceptions may be made so ask your Rabbi if this pertains to you. However, don’t think that the lady that nurses in a public bathroom is frummer than the one that does so on a park bench fully covered — it’s really not that simple.