As the title says. I've been fascinated by the city ever since first hearing about it on Mike Duncan's "The History of Rome." Is there a definitive book about the city's history?
I've heard good things about Pat Southern's Empress Zenobia, which was written to be accessible to a general audience but by somebody who knows her stuff. If you are up for it, Andrew Smith's Roman Palmyra is very good but very dense.
Richard Stoneman's Palmyra and its Empire is, as far as I know, the most widely available general work on the topic. I hear it is well written but somewhat sloppy historically: for example, it takes the somewhat problematic stance that Zenobia was a native anti-Roman insurgent rather than a more complicated modern perspective. Still, it would certainly be a good place to start.