We’re pulled towards the south - Seville, Granada, Cordoba, the Moorish history and a bit of flamenco - but worry we’d be skipping the essentials by leaving Madrid and Barcelona for another time. Would you give a first trip to Andalusia, or is that a mistake?
Southern Spain is one of my favorite destinations and honestly, it has it all: the best weather, incredible music, rich culture and history, and beautiful beaches. Andalusia as a first trip is absolutely not a mistake. Seville, Granada, and Córdoba are all stunning in their own way. Make sure you book the Alhambra in advance, it sells out very quickly. And if you can, add a day in Cádiz. It was my person highlight 
Hi, @carol
As a Spaniard from Madrid, my personal advice, & even loving the North Coast:
I agree 100% to what @SprightlyFjord told you. Especially abour the Alhambra ticket. You cam come to Madrid & Barcelona later.
Depending on yout tolerance to warm weather, you shold rather visit Seville & Córdoba between end of September & April .
San Sebastián (and Santander) in the North Coast is very beautiful too & less warm), just less “typical” Spanish.