The vast majority of the books can be found in Scholomance and the Scarlet Monastery, so a run through both of those instances (you can easily solo both at 80) will get you many of the books you need. From there it's time to travel the world -- Brill, Southshore, the Eastvale Logging Camp, Duskwood, and Booty Bay, and a few other places, depending on your faction (Alliance seems to have a little bit of an advantage there, as Stormwind and Orgrimmar have nice libraries. There are a few good books in Undercity, but the Orcs and Tauren aren't much for book learning, apparently).
Seems totally doable in a quick afternoon, and while you won't really get anything but the 10 achievement points (and probably a nice chance to pick up some more of the old Azeroth explorer achievement), why else would you do this, other than to brag about it. Whenever anyone argues that you don't know your Azeroth lore, you can just point them to your Armory page, and tell them to check the part about you being Well Read.