You are right, the best photos of Alhambra can be shot from Mirador San Nicolas. If you are a photography enthusiast, be sure to be at Mirador de San Nicolas before sunset and make sure you have a tripod.
If you are lugging your tripod, it will be better to take a taxi to Mirador San Nicolas. It should be less than 6 Euro from Granada city centre.
If you are not carrying a lot of luggage, then take Granada city minibus #C1 from Plaza Nueva to Mirador San Nicolas.
Route #C1 is a circular Albayzin bus tour, departing from Plaza Nueva once every 8 minutes. For Mirador de San Nicolas viewpoint, get off at San Nicolas church bus stop. You can also board the less frequent Route #C2, which also includes a side-trip to Sacromonte.
The most interesting way to reach the San Nicolas viewpoint is to walk up from Plaza Nueva. It is a 20 minute walk thru some of the most interesting sights: Moroccan eateries, teterias (Moorish tea rooms) and catholic churches built on the foundations of earlier mosques.
If you walk to San Nicolas viewpoint, you can be assured of many sights that will keep you and your camera busy.
Mirador San Nicolas in the morning
Morning time at Mirador San Nicolas can be a treat if you start early and reach just before sunrise.
The access through the Albaicin and the viewpoint of Mirador San Nicolas itself, are totally different in the morning, silent without the tourist hordes.
Photography at Mirador San Nicolas
Especially if you are into photography, morning can be a unique time to photograph the Alhambra against the Sierra Nevada range.