One thing to note is that the ancient city of Italica was enormous encompassing the old town of Santiponce (where the theatre is located) and the archaeological zone that can be visited where most of the main sites are. The opening hours are very generous though it is closed on Mondays. The tourist zone is quite large you need to backtrack a bit to see everything as the main site is a grid system. Try to see everything listed in the pamphlet as they are quite worthwhile. You can skip the lake which is relatively modern (unless you want to see the nature) and the Traianeum which is quite historical but fenced off so much that it is hard to see (as of Feb 2020).
Points of interest
Teatro romano de Itálica Santiponce
not sure what the opening hours might be for this and the adjacent municipal museum, but it looked rather dead when we swung by