Silver: Ashenvale, northwest of Splintertree post, along the river. Also near the bear cave near the road junction.
Iron: Literally everywhere, but if you want to focus, 1k needles - harpy cave and wyvern perch.
Mithril: Again, many places have abundant veins, personally I found a lot around the bug cave in Shimmering Flats.
Disclaimer: None of these spots are Blizzlike[citation needed], the amount of spawned veins at once is (used to last I checked) be much higher than intended. If that bothers you, do not mine them
. Also, for the record, I haven't mined them ever for those reasons
.
P.S. If fishing for exploits to fix, it's not subtle enough
.