A big "Yes" to San Juan de Dios. Don't miss it; it basically defines "over the top", and that's a good thing when you're a tourist (in my view).
I had plenty of time in Granada so I opted to buy the Granada Card. I think I managed to get to almost all the covered sites. I'd suggest looking at the list on the Granada Card website to see what sounds appealing. Walking around the Albaicin is interesting; you'll see some of it on the way to some of the Granada Card sites.
If you like art, I think you'd enjoy the Rodriguez-Acosta Foundation. I think some Alhambra tickets give you a bit of a discount at the foundation on the same or next day. I lucked out and walked in on a free-entry day just 15 minutes before there was to be an English-language tour. I don't remember how much of that schedule info is on the website.
Because of your timing I want to warn you that this year, May 1 was the day nearly all the Granada tourist sites shifted from their winter hours to their summer hours. I don't know whether that practice occurs in the other Andalucian cities, but it was a bit of an issue for me in Granada. The tourist office (otherwise helpful) didn't have any information about the new schedules and didn't even seem to know things were about to change. What happens on the day of the change is that there are new or much-expanded mid-day closures and sites are open later in the evening. I don't remember whether opening times also change.
