Target pharmacies were bought by CVS. No Walmart in NYC, nor the other chains that you mention. NYC is dominated by Walgreens, Rite Aid, Duane Reade, CVS.
You aren't going to match Walmart on $4.00 generics and have success, but often times independent chains get better discounts on everything else than many of the major chains.
Aaah, that I did not realize. But still, it seems like there's a fair amount of competition among pharmacies in the general sense. I suppose that in specific geographic locales that may not be as true though.
And I'm not saying that this merger is unilaterally a "Good Thing" or anything. It just doesn't strike me as a place where anti-trust specifically comes into play.