This reply was updated on 14th July 2014.
There are some red minibuses in Granada which are specially designed to go around the narrow streets found in the old part of town.
They have circular routes and it is even not a bad idea to just get on one for the ride.
The C1 and C2 minibus go around the Albaicín and the C3 and C4 go up to the Alhambra.
There are maps of all the routes on this page.http://granadainfo.com/alhambra/eng_minibus.htm
The most notable stop on the C1 and C2 minibus route is Mirador de San Nicolas which is probably one of the best views in the world..
See pictures here.http://granadafoto.net/index.php/Plazas/Mirador-de-San-Nicolas
Start at 7.50am and go on until 23.00
The frequency is supposed to be every 7 minutes but it is more like 12 minutes.
If you are staying at a hotel or apartment on the route it many be a good idea to get a "bono" ticket.
This is a ticket valid for several journeys.
The bono cards are available on the bus itself.
Note: These prices are from 2010.
1 Journey is about 1.20 euros.
It costs 2 euros for the card itself. (this is refundable if you return it)
10 euros gets you 15 trips
One card can be used for several people.
i.e.: you can get on with 5 people and pay for all of them with one card.