Sheraton Miami Mart area shopping options?

We will arrive fairly early on a Sunday, a day prior to our cruise. We would like to pack light for the flight down and then acquire a bunch of things that afternoon that are heavy. My wife is very particular about her shampoo and body wash (won't use hotel or cruise ship stock) and there are a few other heavy items we could get after we are there.

What would be the nearest shopping center with both grocery store and possibly some clothing options? A Super Target or Walmart SuperCenter would fill the bill or else a mall with a grocery store near by. About how far away would it be so we can estimate the cab fare? Also...would hours of operation be different on a Sunday afternoon?

Or...we are not averse to public transportation and could catch it from the airport (via hotel shuttle) so if there is a route from there to a shopping center that might work too? I understand Miami Beach allows liquor sales on Sunday but Miami does not. What other suburbs allow liquor sales on Sunday? This too could be a substantial weight savings.