I did more testing.
I tried Safari for about 10 minutes, browsing sites like Facebook, YouTube, Apple and my email...then closed the window, and shut the lid. The computer didn't sleep for 30 seconds. I opened the lid, quit Safari, closed the lid (leaving only Mail and Finder running). The computer went to sleep after about 5 seconds. I opened the lid, ran Google Chrome for 10 minutes, viewing the same sites...closed the window, shut the lid. Computer didn't sleep for roughly a minute. If I leave a window open in Chrome, the screen stays on, the computer stays on, though the lid is shut, and the computer won't sleep at all (if I do this in Safari, the computer takes about 30 seconds to sleep, with the screen staying lit until then).
Yesterday however, I didn't have any windows open (though Chrome was still running) when I had the issue with the screen staying on and the computer not sleeping.
In the past I've reset the SMC because my cooling fan is running a little high.