In general, in the US it is legal to take photographs in any "public" property (eg, streets, parks, etc), unless it is somewhere that there would be an expectation of privacy (eg, toilets or changing rooms, etc).
However shops and shopping centers are not "public" property, they are private property that is opened to the public and the rules are thus a little different.
In general it's still OK to take photos in a private place open to the public, unless you have have been told not to. That might include a sign at the entrance or within the shop saying no photographs, but also includes a representative of the store asking you not to take photos. Legally if you refuse to comply with the conditions of entry - including not taking photos if requested - then you are trespassing and can be asked to leave, or if you refuse the police can be called to remove you from the property.
Supermarkets in particular are normally fairly touchy on the subject of photographs as they have historically been used by competitors, especially for price matching.