The hotel which best fits the bill is Hotel Guadalupe which is about 300 metres away from the entrance to the Alhambra.

The car park is about 200 metres away and the is very easy to get to.

There is a map of the motorway system around Granada on this page.
http://granadamap.com/
As you can see you just get onto the circunvalación (the ringroad)
There are many signs to the Alhambra which will take you to the Alhambra car park.

The Guadalupe hotel does a cheap menu del dia which would be good if you have 5 people to pay for.

More info about guadalupe hotel here.
http://www.granadahotel.com/guadalupe.htm

 
The only thing you would have to decide is if you want to go into Granada itself.

If you do want to go into Granada and you only have very limited time a good idea would be to get on the 32 minibus which will do a circular route and bring you back to where you started.
More info
http://granadaforo.com/getting-around-in-granada/alhambra-bus-and-albaicin-bus/


You could get off the 32 minibus at the Mirador de San Nicolas and then have a wander around the old part of town.