I go regularly to Southern Spain. Within walking distance are Super Cor (El corte Ingles), and Mercadona. Also Aldi and Lidl, but they are at home, so I'm not too bothered with them when away.
I love both, but the SuperCor (formerly Supersol) is like Aldi for prices and I just love their make up and toiletries, especially the Revuelle brand, it's cheap as chips. In fact I bought a nail polish called SOS repair for brittle and broken nails, it was around €2 and folks, I painted those talons last Friday, and there ain't a chip to be seen yet. It is super stuff. I'll be stocking up when I get there later in the year.
I also like the big tubs of flavoured cappuccino, Caramel, Vanilla, etc. so moreish and gorgeous and cheap as chips. Lots of other stuff too, too many to mention.
But you can't beat Mercadona for fresh food and a huge range. A ten minute drive away is Carrefour. But honestly that place is just SOOO big I get the heebie jeebies and am overwhelmed by the sheer size of it, so don't use it much apart from big ticket items like replacing a busted suitcase etc.!
OP, enjoy your trip and your shopping, you've got lots of ideas above.