I think a day trip to Granada from Marbella is perfectly OK and in fact, I almost attempted this day trip but in my case, I was in Malaga, which about 30 minutes closer to Granada than Marbella. However, after much debate, I decided to make it a 2-day trip and also visited the Mezquita in Cordoba. From what I remember, the trip from Malaga to Granada took about 1 and 1/2 hours and so from Marbella, it should be about 2 hours. After visiting the Alhambra and Granada, at the end of the day, I drove about an hour to Jaen and stayed at the parador in Jaen, the Castillo de Santa Catalina. Excellent parador. By the way, if you ever doubt that Spain produces more olive oil than Italy, driving through Jaen, will convince you otherwise. You drive for hours and hours and miles and miles and all you see are olive trees. Anyway, from Jaen, I drove to Cordoba the next day and saw the Mezquita. I personally think you should visit Cordoba. Although the Alhambra in Granada is much more intriguing that the Mezquita in Cordoba, I liked the city of Cordoba betten than Granada because it seemed to have more character.

And so, in short, though a day trip from Marbella to Granada will probably take about 2 hours each way and is within reach, I would suggest that you make it a 2-day trip and also visit Cordoba. Just my two cents worth!