1) SEVILLA: One of the most beautiful city that the region of Andalucia has to offer is for sure Seville. Here you can explore the many neighborhoods of the city like Triana the place of the toreros and artists, Nervión, Santa Cruz: a very picturesque and characteristic "barrio" which was a jewish neighborhood.
The main attraction of Seville are for sure: la Torre del Oro from the top of which you can also admire the landscape of the city, the Catedral and the Giralda, the Isabel II bridge, which connects the city centre to the Triana neighborhood, the Alcazar, Las Setas and of course Plaza de Espana, situated on the edge of Maria Luisa Park, this square is plastered with vibrantly colored azulejos and encircled by a 500-meter canal.
2) GRANADA: Another beautiful city with a special atmosphere is for sure Granada, it offers a vibrant environment. The main attraction of the city is fo sure the Alhambra as well as the Generalife, one of the world's most breathtaking monument, so a visit there is a must if you have a chance to go to Granada.
There are also many "miradores" which are strategic viewpoint where you can admire the city from above. One of the best are Mirador San Nicolas and Mirador de San Miguel Alto.
Granada has also many neighborhood worth visiting, such as Albaicin, Realejo and Sacromonte.
3) CORDOBA: Going to Cordoba and not visiting the Mezquita Catedral would be like leaving the Alhambra out of a trip to Granada: it is the city's greatest monument.
Another main attraction is the Roman bridge which crosses the river Guadalquivir.
Another good reason to pay a visit to the city of Cordoba are the prettiest and most unique patios, I would recommend going during the period of the Feria de los Patios. I would suggest to visit also the Alcazar de los Reyes Cristianos, one of the city's key architectural landmarks.
I hope that during your stay in Spain you will have the time to visit all these beautiful cities!