I would like to know the nearest hotels to the Alhambra because that is my main reason for visiting Granada

You should remember that the Alhambra is above the city of GRANADA and it may be more interesting to get a hotel right in the centre of Granada near to Plaza Nueva.

Here are some links to lists of hotels organised by the distance to certain locations.

The nearest hotels in Granada to the Alhambra are here:
https://granadahotel.com/near_to_alhambra.htm

The nearest hotels in Granada to Plaza Nueva are here:
https://granadahotel.com/near_to_plaza_nueva.htm

The nearest hotels in Granada to the bus station are here:
https://granadahotel.com/near_to_bus_station.htm

The nearest hotels in Granada to the train station  are here:
https://granadahotel.com/near_to_train_station.htm