D1–D2 Madrid → D3 Toledo → D4 Seville → D5 Granada → D6–D7 Barcelona. High-speed AVE trains take about 2.5 hours from Madrid to Seville, buses or trains take around 2.5–3 hours from Seville to Granada, and flights from Granada to Barcelona take about 1.5 hours.
A 33-minute high-speed train ride from Madrid, Toledo is known as the “City of Three Cultures” and was once the ancient capital of Spain, where Christian, Islamic, and Jewish cultures blended. Visit Toledo Cathedral, Alcázar of Toledo, and The Burial of the Count of Orgaz at the Church of Santo Tomé. Return to Madrid in the evening.
Take a morning high-speed train to Seville. See Seville Cathedral and La Giralda Tower → Royal Alcázar of Seville (a filming location for Game of Thrones) → Plaza de España → Watch a flamenco performance in the Triana district in the evening.
Head to Granada. Key sights include the Alhambra (book tickets well in advance, especially for time slots including the Nasrid Palaces) and the Generalife Gardens, with views of the Sierra Nevada mountains. In the afternoon, explore the Albayzín neighbourhood and enjoy the sunset over the Alhambra from the Mirador de San Nicolás.