Aside from the Alhambra, are there any other places in Granada that would need advanced tickets?
Nope, but it can't hurt to book any place in advance that you know you are definitely interested.
Actually, it can hurt. If you have to cancel or delay the trip, you're highly unlikely to get your money back. I see no reason to buy sightseeing tickets ahead of time that will be readily available on a walk-up basis when a tourist gets to town. Tours with specific guides are a different matter entirely, of course.
Agree with previous posts—Alhambra is a definite well in advance
No to other places but if it is someplace you really want to visit, do it in advance. After all, you never no when three bus loads of Yanks will show up.
If tickets to the Alhambra are sold out, the Granada card includes admission to the Alhambra, and other areas as well as some transportation trips.