We've already gotten some lovely suggestions for Sevilla and Barcelona, but just to check in once more - what are your favorite restaurants; from elegant and special to easy going and tapas favorites. We will be in:
Madrid
Cordoba
Seville
Granada and
Barcelona

our mouths are watering...

We love More in Madrid's Salamanca neighborhood.
In Seville, we just popped into tapas restaurants.

<easy going and tapas favorites>

Madrid, Casa Revuelta: https://no.tripadvisor.com/Restauran...ta-Madrid.html
Córdoba, Taberna El Gallo: http://azahar-spain.com/azahartapas/taberna-el-gallo/
Sevilla, Bodega Diaz Salazar: https://www.tripadvisor.com/Restaura...Andalucia.html
Barcelona, La Perla: https://www.tripadvisor.com/Restaura...Catalonia.html

Madrid,

Abraham Garcia in Viridiana does his own thing. He does not follow the trend.
http://www.restauranteviridiana.com/

Maria Marte left her home in the Dominican Republic in 2003 to earn a living. She took work in El Club Allard, where she was offered a job washing dishes by the hour. Today, she is head chef of this two Michelin-starred restaurant.
http://www.elcluballard.com/en/

La Catapa. Tapas bar and restaurant.
https://www.tripadvisor.com/Restaura...pa-Madrid.html

"elegant and special" restaurants.

Check out the Guía Repsol for your cities, the Spanish equivalent to the Michelin guide with the best knowledge of the local food scene. https://www.guiarepsol.com/es/la-gui...-restaurantes/
Here are for example the 24 Guía Repsol restaurants in Sevilla. The highest ranking is three soles/suns: https://www.guiarepsol.com/es/la-gui...locality=|6964

I recommend to make a reservation at Tickets in Barcelona, the paradise version of traditional tapas style restaurant run by the Adrià brothers of the world's by far most awarded restaurant this century, now closed El Bulli. Very affordable Tickets was up on the list of the world's 100 best restaurants after one year (#77), and jumped this year to #25. http://www.theworlds50best.com/

The basic concept is traditional tapas prepared and presented as you never would imagine and with tastes to the maximum. Iberian ham, Spanish cheeses, olives, croquetas, tomatoes, anchoas, shellfish, Iberian pork etc etc plus some surprises from out of this world. Just tell the waiter how much you would like to spend and what kind of food you like, and then leave it up to the kitchen to make it an evening never to forget. Have had both lunch and dinner here, some 15-17 small dishes each with wine/cava/beer has been some 70-80€ pp. Lived very much up to the high expectations.

You can normally only book online and only two months in advance. Tables are literally gone 10 minutes after midnight two months prior to every day year around, so you have to be online on midnight Barcelona time two months ahead to book a table. http://www.ticketsbar.es/web/en/

22 Michelin star restaurants in Barcelona, but you'll find more and perhaps more interesting options in the Guia Repsol. https://www.timeout.com/barcelona/re...michelin-stars
69 Barcelona restaurants mentioned in the Guia Repsol, 36 of them with suns. https://www.guiarepsol.com/es/la-gui...locality=|3005

I can also highly recommend Somodó in the Gracia district in Barcelona, perhaps the best gourmet deal in town. The lunch is a bargain, and we had an excellent late night meal here a few months ago. http://www.spottedbylocals.com/barcelona/somodo/
http://www.somodo.es/

oh my goodness, these are awesome, thank you - so many wonderful choices

Barcelona - We spent a week there last year and had great meals every night. All of these are in the Old Town , either in El Born or the Gothic Quarter: Tast Ller was fantastic but you must make reservations weeks in advance. They have a set tasting menu with wine parings. The filet with truffled demi glace at Café De L'Acadamia was outstanding. We ate there twice. Tapeo was our favorite tapas bar. Arcano and Llamber were very good. Great restaurant city.

Just returned from our 4th visit to Barcelona...also visited Seville for the 1st time on this trip. In Seville, we did a spur of the moment day trip to Cadiz for a 4 hour city bike tour with Sights & Bikes - highly recommended/unexpected highlight of our stay in Seville.

Not sure where you're staying in Barcelona? So many wonderful restaurant choices...listing a few of our favorites in Eixample within walking distance from our B&B. All popular so you will need reservations. I've read through your itinerary - you're going to have a great trip to Spain!

BARCELONA (Eixample district/must reserve)
The Sopa Boba - fun vibe, great waitresses, tapas/entrees with a modern twist, we sat at the bar
Paco Meralgo - our go-to favorite, try to sit at the bar
Mont Bar - highly recommended by a foodie guest at our B&B
Etapes - chef & tasting menus or order a la carte, recommend booking an outdoor table, nice location on Enric Granados, great service, very personable & wine savvy manager, Didac
Primavera Cafe - cute bar with a fun, local vibe & exceptional Gin Tonics

SEVILLE
Zoko Sevilla - South American/Asian fusion, modern vibe, great wait staff, try to sit at the table that faces the chef, tuna seared with a blow torch - amazing

MADRID
Taberna La Carmencita (Chueca district) - ate there twice 3 years ago on our 1st Spain trip, food/service/ambiance - all excellent

Just got back from Barcelona, I don't think we had a bad meal! Some highlights were the tapas at Vinitus and the paella negra at Boca Grande. Vinitus can have a wait, we arrived at 730 PM for dinner and shortly after the wait was up to 45 minutes. Boca Grande takes reservations and also fills up after 8 PM. I was happy as long as I could have pan con tomate and jamon iberico for starters . We also enjoyed snacking throughout La Bouqueria, lot's of great little stalls to grab a quick bite.
Have fun!