How to get around Andalusia:
The best way to move from city to city, is by bus or train. Rental cars might be comfortable, but they are more expensive and to be honest, there is nothing special to see on the way.
The best way to get around Granada is on foot. Public buses and microbuses are a good alternative for visiting the Albaicín and Sacromonte, and especially for going up to the Alhambra, allowing you to avoid the trek uphill.
The best way to get around Seville is also on foot. Biking is a very good alternative for crossing over to Triana, visiting parks or riding along the river. If your hotel does not rent or lend bicycles, the city's public bike service (Sevici) is an option. It works exclusively from the service stations next to the stops using a credit card.
To go to the train stations or airports, the bus is a convenient option.