My advice to you is to at least give 2 days for Granada... The best way to get there is by bus. There are several bus companies, I recommend is
Continental Auto (aka Alsina Graells). Dedicate a full day to the Alhambra, if you consider yourself a quick sightseer you could do the entire Alhambra in about 4 hours if you take more time give it 5-6 hours. Which means that the best way to do this is to get a morning entrance to the Alhambra, even better yet... I had my hotel reserve my tickets, so I got to the Alhambra skipped the huge line and went straight to the reservations window, told the person my name and he had the tickets there ready... paid and got in by 9am.. was out by 2pm. Ah! Dont bother on going up the alhambra hill on foot.. spare yourself the pain and catch the Alhambra Bus right on Plaza Nueva, its #31 and #32 if im not mistaken just ask the driver.
Ah... After doing the Alhambra rest.... then head out again if your feet allow it.
Granada's Cathedral & Sacristia (both separate entrances) dont take more than 90 minutes, I did both in one hour. Both are worth it! The Cathedral is just HUGE.
I did those 2 places in one day... the second day you can explore the maze of little streets in the Jewish quarter (Albaicin) and then Granada town itself its fun
Hope this helps!
Joel