Looking for some help in planning the optimal itinerary for a trip beginning and ending in Seville, seven full days not counting the first day late arrival in Seville, and early departure on day 8 (trip is late January). We don't plan to rent a car, and aren't in agreement on whether we should use Seville as a spoke for day trips to Cordoba and Granada, or stay over in one or both of those cities. We also are interested in visiting either Cadiz/Jerez or Gibralter. Originally had also thought about a day trip to Tangier but that seems like too much energy for a day.
Would appreciate any feedback on anyone's thoughts for the best way for us to get a good experience of this region - realize it's a short trip (and we cannot change the duration). Realize that we can't do it all, but we're comfortable with a busy itinerary and pack light. We're equally interested in culture/arts/museums as on natural beauty, small towns, etc.