This is the start of the path they called Paseo de los Tristes (Promenade of the Sad Ones) because the funeral processions used to pass here en route to the cemetry. The river to the right, just under The Alhambra, is more like a stream (at least it is in summer!). Some even have gone to proclaim is as the nicest walk on earth. Not true. It's a pleasant walk although it's not pedestrianised, surprisingly, but nothing more than that for me.
However, as you carry on, and go up Cuesta del Chapiz, on your way to Sacromonte, on the right, you'll find a gorgeous garden. Free entrance. This is Palacio de los Córdoba (sometimes spelled with a "v") and it's not even listed here. It's a peaceful place, great to stop in the shade, take a breather, look up to the majestic Alhambra, listen to the birds and the sound of the fountains, before you carry on climbing up the road. Here's their website: http://www.andalucia.org/en/cultural-tourism/visits/granada/monuments/palacio-de-los-cordova/
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