For the most breathtaking view of the Alhambra, you have to make your way up to the Mirador de San Nicolás in the heart of the old Albaicín quarter. The atmosphere here, especially as the sun sets and bathes the fortress in golden light, is absolutely electric with the sound of flamenco guitar filling the air. Getting here is part of the adventure; it's a charming, if steep, 20-minute walk up winding cobblestone streets from Plaza Nueva, so be sure to wear comfortable shoes for the climb.
If you decided to catch a bus to get there, I do recommend that you walk down. It takes around 10 minutes and it's a beautiful walk across cobblestone streets. Remember though, that this neighbourhood is not the most stroller-friendly place! Cobblestone has its good and its bad things!