lymichie,
I assume that your lodging on Doctor Velasco is an apartment. If so, then I suggest that you cross over to the other side, and walk west on Calle Atocha and then east into the Barrio de las Letras for a better choice of dining. There's not much around you on that side, near the Royal Botanical Garden. On another thread Revulgo and I left some recommendations for those staying at the Catalonia Las Cortes

Barrio de las Letras Madrid
Vinoteca Moratín on Moratín
Ocafú Taberna Gallega on Prado
Triciclo (must reserve online!) on Santa María
A Mano on Plaza de Matute
Chocolat on Santa Maria for churros & chocolate, recently featured in the Madrid episode of "José Andrés and Family in Spain" on Discovery Plus
Estela Hojaldre at Plaza Jesús for gorgeous pastries

Sevilla
Bodeguita Romero
Casa Morales

Córdoba
Casa Pepe de la Judería, also recently featured in the Madrid episode of "José Andrés and Family in Spain" on Discovery Plus
Regadera on the Ribera
Taberna Salinas Ribera

Granada downtown
Nothing close by---walk down the set of staircases and get to the Plaza del Ayuntamieto on anywhere downtown, then take the minibus back up to the Alhambra Palace hotel and walk back down to the Carmen

Cunini and Oliver on Plaza de la Pescadería for seafood or just tapas at the bar (remember that you'll get a complimentary tapa with each drink order in Granada)--
(Bordain filmed at Oliver)
Los Manueles Bib Rambla on the adjacent Plaza Bib Rambla
Alhambra on Plaza Bib Rambla for churros & choclate
St Germain near the cathedral for wines and tapas
Taberna la Tana for wine & tapas on Calle Rosario
Los Diamantes for seafood dishes and fried fish, 4 branches, the largest on Plaza Nueva and another, smaller on Calle Rosario
Chiquito for very traditional Granada cuisine with covered outdoor terrace
López Mezquita on Reyes Católicos, an iconic pastry shop

Thank you, Maribel. Yes, the Sevilla and Madrid stays will be apartments. We will be staying a week in each place and thought it would be nice to have a bit of room. The reviews are good and mentioned the ease of accessibility to different sites in town. Your thoughts? I do have the thread you noted with the restaurant recommendations near the Catalonia. Thanks! And as always, appreciate the new notes!

I think the location of both apartments is fine, especially in Sevilla, which will get you out of the most heavily touristed zone, yet will still be easy walking distance from the cathedral, Alcázar, Murillo gardens, Iglesia del Salvador, the river and the walk over the bridge to Triana, plus the great tapas bars of the Arenal quarter close to the bullring.

Cordoba: We stayed at Las Casas de la Juderia and we had a delicious dinner at Regadera, located at Ronda de Isada 10. One of the best meals of our trip. Also had dinner at Mercado Victoria, where you can choose from different food stalls. We tried Arabian food from a Syrian refugee. Had tabouli, lamb tagine, and a chicken pastrela with cinnamon sprinkled on top. Delicious! Also tried some Japanese food.

Granada - loved our dinner at El Trillo Restaurante. It was an uphill walk, not too difficult, with views of the Alhambra.

Seville - La Azotea in Barrio Santa Cruz. Another favorite. We ate here twice!

Madrid - we stayed near Calle de Jesus with all its tapas restaurants. Some favorites: La Dolores at Plaza de Jesus 4; Cerveceria Cervantes; Taberna Macieras; and Taberna de la Daniela Medinacelli.

Appreciate your thoughts!

Now you have a second for Regadera!

For Alhambra views around the Mirador de San Nicolás in the Albaicín, in addition to El Trillo, there's also maitaitom's favorite, Carmen de Aben Humeya. Both are lovely.

I too love La Azotea, but prefer the one in the San Lorenzo district at Conde de Barajas 13, rather than the one in the Barrio de Santa Cruz at Mateos Gago, the "restaurant row". Less crowded but one still should reserved

Ditto to the tapas bars that Karen mentions, all in the Barrio de las Letras. We enjoy La Dolores for draft beer, Cervecería Cervantes for the same and their wide selection of tostas or canapés and salads. At Cervantes, there is table seating on marble tables and a complimentary aperitivo of olives or cheese with your drink order. It's always crowded, especially after mass gets over across the street, so we go early when they open at noon or early in the evening. Taberna Maceiras is cuisine from Galicia. La Daniela is famous for its cocido served in the dining room. Just tapas at the bar.

Karen, thank you! I’ve read about a few restaurants you’ve mentioned and I’ve noted the new names! La Atozea appears to be quite the spot in Sevilla! The Mercado Victoria sounds interesting… Gracias!

Again, Maribel, your thoughts on locations noted.

Didn’t know there were multiple La Azoteas… might have to try both…

i really can’t thank everyone enough for all of your recommendations and thoughts!
I appreciate the time and effort that has been put into these posts.
This trip feels comfortable and quite manageable. And it’s because of the information I’ve gleaned from the posts.
Thank you all!

For incredible seafood straight from the Costas, there's La Barra de Cañabota, the casual, less expensive sibling of the now Michelin-starred mothership, Cañabota, or closer to your lodging, La Barra de Inchausti.

https://azahar-sevilla.com/sevilleta...a-de-canabota/
https://azahar-sevilla.com/sevilleta...-de-inchausti/

Bravo!! Another one added o the list!!

Has your itinerary been finalized? I’m also staying the same amount of nights, could stretch it to an extra night or two. I also like to to travel at a slower pace. Would like to copy your route.

More or less. But I'm not moving slow really. I'm staying 3 or 4 nights at most and often just 2 nights in some places.

We’ll arrive in Madrid mid afternoon. We’ve taken the advice of Maribel and will spend our first night in town.

Madrid - 1 night
Cordoba - 4 nights, which allows 2 full days, and half day on arrival and departure days. We will be traveling by train.
Sevilla - 6 nights, which gives us 4 full days, one of those days, we will hop down to Cadiz. And again half day on arrival and departure days.
Granada - 4 nights, yielding 2 full days with half days on arrival and departure days.
Madrid - 7 nights, 5 full days with one day traveling down to Toledo. We are not certain if we will visit any other areas outside of Madrid. Most likely just stay in Madrid and wonder…

So that’s our trip in a nutshell…

P.S. Thanks again everyone!!!

Ooops… add a FULL day onto each stay…

Just read this wealth of information here as I plan my own trip for this fall finally! Love all of the suggestions -- you guys are amazing!

I am a bit late to the game as I would like to stay in the Santa Cruz neighborhood for 3 weeks in late September/early. October and many apartments are already booked!

Thank you for all the inspiration here!

What is your plan to get from one city to another?

I haven't read all your responses, but wanted to chime in that we LOVED Seville. We stayed 5 nights, in a lovely apartment.
We had thought of making a day-trip, but we enjoyed just walking around Seville, so we stayed there.

Two restaurants we found and loved:
San Marco
https://restaurantesanmarcosantacruz.es

El Pinton
https://carta.elpinton.com/en

We enjoyed a flamenco presentation at the Flamenco Dance Museum:
https://museodelbaileflamenco.com
It is a very tiny little place, so get there early. I forget if we were able to get reservations.

Thank you! We will add the restaurants to our list!!!

Trip report! A summary at least :)