As long as your breast is not exposed, there is no prohibition against nursing in public unless local feeling is clearly against it. The ability to nurse in public gives the mother much more freedom to pursue her normal life style and thus should be encouraged.

Modesty is maintained by covering yourself with a blanket, your shirt, or a sweater that drapes over your shoulder while breastfeeding. You can even purchase a "nursing apron" designed for this purpose; you may also be able to find clothing with an arrangement of slits and flaps to facilitate modest nursing. In a restuarant, you can often sit with your back to the other patrons. With practice, breastfeeding in public can be done discreetly so that only other knowledgeable nursing mothers will know what you are doing.

There is no need to cover the mezuzot.