Well if you didn’t have mining before, then you didn’t have the ‘find minerals’ skill, which puts a yellow dot on your minimap when the ore is nearby. Granted, as you said, in SW and IF areas, you can often physically see the ore vein, but that doesn’t mean there aren’t any around NE starting areas.
However, since I consider that Elwynn/Westfall and Dun Morogh/Loch Modan are much smaller starting areas than Darkshore/Astranaar, I really prefer to mine in those 2 areas, and I would suggest the same for you, even if you start up as NE.
Eg, keep the skills you want and around lvl 10 or 15, when you’re ready to do some traveling (earlier, possibly), then just head over to those other areas.