Seville and Granada-what neighborhood to stay in

I enjoyed staying just above the Setas/MetroParasol in Sevilla. It's a residential, local area, but steps from the center. (The tourist core is on the other side of the center.)

We like Gracia in Barcelona and we absolutely LOVED being over in Triana in Sevilla. Our Airbnb was just a few blocks south of the Mercado de Triana

Thanks! I can’t quite figure out where the Setas area is.
Why did you like the Triana area?
We would like an area that feels like a cosy neighborhood with greenery. Any ideas on that in Seville, Granada or Cordoba?

Anyone have neighborhood ideas for Granada. Again we are hoping for a quietish street with a park for walking in greenery nearby. Also not too far from what we might want to see on this first trip to Granada.

Setas isn't an area, it's a monument/sight.

We stayed in the Realejo area last time we were in Granada and loved it. It is very residential, non-touristy, with a nice mix of shops, tapas bars, and restaurants. It is only a short walk to the Plaza Nueva, Cathedral, etc. You can walk up to the Alhambra if you choose (we've done this; it's not a long walk, but it's very steep uphill), or you can catch the bus -- I think at the Plaza Isabel la Catolica (verify this; it may have changed) -- or taxis are very cheap.

This was our apartment, which was excellent. The listing is for 4 2-BR apartments (we had 10 people and rented them all), but you can message the host to ask about the rate and availability for individual apartments. The building is on a really nice square with good restaurants, plus a fruteria, bakery, and small grocery store on the same block. But still very quiet inside the apartments.

https://www.airbnb.com/rooms/29879241?sourceimpressionid=p316863283794JpBEe1hbxdaGxPD

La Carmen de los Martires is either in or adjacent to the Realejo. It has lovely gardens that you can wander (and peacocks!).

There is also a giant park above the Alhambra that has spectacular views. From the main Alhambra entrance/taxi dropoff, head up the road and there will be entrances to the park (La Dehesa del Generalife) on the left. We spent a few hours last year on New Year's Day walking a big loop around the park; it was lovely -- old olive groves, views of the mountains and the Alhambra and Granada far below, families picnicking all over the meadows.

We loved our March stay at Hotel Amadeus in Seville. It's in the Santa Cruz neighborhood area near the Real Alcazar, but also a walkable distance from the large Maria-Lusia Park and the Plaza D'Espana. And I would heartily endorse the previous suggestion about the San Nicolas Viewpoint in Granada. The views are magnificent and the atmosphere is very inviting.

In Seville last fall, we stayed at the El Rey Moro Hotel Boutique in the Santa Cruz neighborhood. A great home base, the hotel was lovely, the breakfasts were delicious, and located walking distance to a ton of places to eat and things to see and do.