What Jazz Is: An Insider’s Guide to Understanding and Listening to Jazz. Jonny King. Walker and Company, New York, 1997.
This is a great introduction to how to think about jazz. It’s also a starting point for knowing and recognizing the work of some of the most influential jazz musicians.
Downbeat is more or less the original jazz magazine, established in 1934. The website is a fantastic source of information on mainstream jazz artists, new albums, and general goings-on in the jazz world.
This was my go-to site for jazz clubs and concerts when I was studying in Paris. I especially love Duc des Lombards, Sunset/Sunside and Le Defender.
Arts Journal isn’t exclusively jazz, but has great material nonetheless.
A little food for thought on the future of the genre is available via NPR.