Not a terrible itinerary but here is my advice:
I would skip Valencia all together and replace it with Granada. Personally I would probably do the beach end in Almería and then go directly to Granada and then Sevilla. Valencia is a really nice city, but it's the kind of place I wouldn't mind living at and I like going to because it's a 3 hour drive away. Your time is much better spent elsewhere.
Another option to add on would be for the AVE from Sevilla to Madrid to stop in Córdoba and see the old city. It's very nice and an afternoon does it justice.
The amount of time spent in any city is good. Madrid may be a bit tight if you want to do Museums, Segovia, AND Toledo. But even so, it's all perfectly doable as the city really comes alive around 8 or 9 at night and while there are some beautiful streets, this city is much more about the culture and the evening/night life than any specific daytime site. Both Toledo and Segovia are plenty interesting. The Segovia train stations are far from the tourist area so I would maybe think renting a car for the day may be worth it and you can stop and see La Granja de San Ildefonso in the morning by way of a nice mountain drive (that avoids tolls).
But yeah, the conclusion being it would be a crime to miss Granada and La Alhambra (book in advance).