Hi Pett! There's a bus from the airport to the bus station which goes every half an hour and costs about 130 Pts. The train goes from the airport too and the bus station is just round the corner from the railway station in Malaga - similar price and also every half an hour, but its a walk to and from both stations. Take the bus and if you have time to kill, there are a couple of good tapas bars opposite the bus station.
You should be perfectly safe, but loke in any city, watch your bags, just in case. Have fun in Granada!
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