Hi Suze, I think that the current version of your itinerary is too jam-packed, even without adding a day trip (I'm counting seven nights).
If you had more time, I would still not recommend doing Granada, Cordoba, Nerja, or Sevilla as day trips - they are too large, with too many things to see - they would require at least a couple nights in each.
There are also no good public transportation options from Alicante to Málaga, the fastest way would be to rent a car.
Personally I would restructure the itinerary like this:
1. Tarragona
2. Tarragona
3. Valencia
4. Valencia
5. Valencia
6. Valencia
7. Alicante
8. Alicante
I would eliminate Málaga as I feel that it is a bit of an outlier here. Why I give so much time to Valencia is that one can rent a car and then use Valencia as a spring board to do some pretty cool day trips.
For example, from Valencia, you could day trip (or side-trip) to:
Cuenca: A UNESCO World Heritage Site, this 12th century medieval town is built on the steep sides of a mountain, which makes for a very unique place to spend a day or two.
-you could also go to-
Peñíscola: Another historic and beautiful town, with its cobbled streets and whitewashed houses, it sits on a big rock that juts out into the sea. The town is dominated by a large Knights Templar castle. It was later home to 15th century Antipope Benedict XIII.