For Granada, the best way is to simply hop on the bus. It's as fast as the train and a lot cheaper. But I'm not sure if you'll be happy with just a day trip to Granada, since the journey between the two cities takes about 3 hours (165 miles). Check out http://www.movelia.es for schedules...but it appears the maximum time you'd have in Granada would be 9 hours. You'd leave from the Prado de San Sebastien bus station in south-east Sevilla, a grubby little place. In July, the buses will be busy, and seating is assigned, so maybe buy in advance over the internet to make sure you're on the buses you want. For Gib, it's even worse. Buses from Sevilla take about 4 hours to get to La Linea, bordering Gib, and the first one doesn't leave Sevilla until 9 am, altho there may be a slightly earlier one in the summer. An option is to spend o/nite in Granada (recommended) and in La Linea (not recommended). Or you could rent a car and leave really early (continued)