There used to be a lot of very cheap flights to Malaga from Newcastle but now there are less.
Just do a google.
Then you need to get a bus from Malaga.
Malaga airport has a special bus stop with buses to the Malaga bus station.
Get off the plane, go to the bus station and get on the bus to Granada.
Once you are in Granada bus station get a taxi from Granada bus station to
the accom or get on a bus into the centre.
Info about bus tickets herehttp://alsa.es
The closest places to the Alhambra are these.
They are just on the doorstep.
They are all about 100 metres from the grounds of the Alhambra just off the Cuesta Gomerez
which goes up from Plaza Nueva to the Alhambra.
It's up a hill so not OK if you have health problems.
The people who run the Alcoba speak English are a good source of local info.
Alcoba A - 800 metreshttp://granadainfo.com/alcoba
Apartment in a beautiful house in the centre of Granada, near Plaza
Nueva just below the Alhambra. Excellent location. The apartment has 1
bedroom (with a double bed), kitchen, lounge with a sofa-bed, and
bathroom. Shared outside patio.
Picasso 3 - 800 metreshttp://granadainfo.com/picasso
Modern duplex apartment for 5 people in the centre of Granada (very
near Plaza Nueva and the entrance to the Alhambra complex). The duplex
apartment has a bedroom with ensuite bathroom and double bed, lounge
with sofa-bed and extra bed, kitchen and bathroom. Air
conditioning/heat pump. WIFI broadband Internet. Washing machine. TV.