There's a bus called Manuel Tienda Leon that goes between the two airports but it also stops somewhat close to the port if I recall. You could see about taking that into the city, getting off and exploring downtown, and then hoping back on to go to AEP. AEP is a quick airport to get through in terms of security.

By AEP if you cross the street and head toward the water there are some decent food stands as well to get a meal better than what you'll get inside!