Insight Please: Madrid-Cordoba-Granada-Seville-Mallorca or Nerja-Barcelona 18 nights

Granada is time-consuming to get to, and I think you'll find it difficult to see the Alhambra and a bit of the rest of the city with only one night there.

Cordoba is about 45 minutes from Seville and 1 hr. 45 min. from Madrid, so if it is to be a day-trip, the day-trip should be done from Seville. I hate one-night hotel stays, so I would not schedule back-to-back one-night stops.

Consider flying from Granada to Palma or vice versa to eliminate one of the awkward Granada legs. (I haven't been to Nerja or Mallorca but would add time to some of your other destinations in lieu of Nerja; Mallorca sounds more special.)

Assuming Madrid is your first European stop, the arrival day may not be worth much. In that case, you really are giving yourself just one day for the city, which is awfully short given your expressed interest in the museums. The Prado is quite large (5 hours for me, as I recall, and I am not a huge fan of Spanish art).

We just got back from Spain and we spent the first three nights in Palma, Mallorca. It was a great place to visit and we barely scratched the surface. Our logic is that we would relax on the beach for the first three days, then get into the mainland with all the sightseeing. If you do go to Palma, I highly recommend one of the afternoon boat tours.

We went to Cordoba on our way to Madrid and that seemed like enough time. Three nights in Seville was perfect for us, I feel like I got to really explore the city. Six nights in Barcelona seems like a lot. Maybe you could get over to Bilbao and other places in the north.

This was our itinerary, although we only had 14 days:
3 nights Palma
3 nights Barcelona
1 night Granada (flew from Barcelona to Granada)
3 nights Seville
3 nights Madrid

I spent 10 days in Barcelona and had to skip a lot. It really depemds on how you feel about museums and modernista architecture.

I have never been to Mallorca, but if you choose the Nerja option...your order is off. Nerja is pretty close to Granada, so I'd go from there.
Madrid to Seville, stay 4 nights and do Cordoba from there - it is only 45 minutes by train.
Then bus or train to Granada. It really needs 2 nights, but it's possible to squeeze it into 1.
Then to Nerja, which is less than 2 hours by bus, closer to 1 if you have a car
Then fly from Granada or Malaga to Barcelona. Nerja to Malaga is also less than 2 hours by bus and I think there are airport shuttles as well for more $$.

Given this, Nerja is well less than half a day of travel. I'd pick it, just because the hassle and wasted time of flying to Mallorca would be annoying to me. Mallorca does look lovely, though.

Past travel adventures include over a week in Mallorca, staying near the port (there are $$$ in those ships), for a cycling trip in early spring. Positive memories. There is night life till 0500. Do not miss the other side of the island. Stayed nearly a week in Nerja area for another cycling trip in an apartment in late spring. Exploring was such a keen experience. Now, where is that roman site? Oh, it is over my shoulder. The area we stayed in was low key. Seasonally it can be a place for Spanish families to stay for their summer vacation. Mallorca may be a bit upscale and set up for tourists and Nerja may be more local (the British do have properties there) and require a car for exploring. The white village nearby is quaint. As all ways, beautiful view of the sea, where ever you choose.