The Oro guest house is in Paseo de los Tristes.

There is a good restaurant right next to where you are staying.

It's not amazingly romantic but the food is good.

Restaurante Azafran
Info here
http://granadamap.com/azafran/

Another place which is very romantic and very near is the Mirador de Morayma.
It has a couple of small rooms with views of the Alhambra which are very romantic.
Info here
http://granadamap.com/morayma/index.htm

I suppose romantic is usually expensive.

For a list of expensive restaurants in Granada
Info here:
http://granadamap.com/places/expensive_restaurants_in_granada.htm