Mithril and Iron in Arathi and Badlands
There are in general two options for Mithril. You can go to the higher zones and pick up some thorium on the way, or you can go to the lower zones to get iron. When leveling your Mining profession, the latter option is usually the best. Here are two routes for farming mithril and some iron in Arathi Highlands and Badlands. In the Badlands, you might want to skip the part to the east, as there are elite dragons there.
Tanaris Mithril farming
Tanaris is a good middleground between small Thorium and Mithril Ore veins. according to databases, there are around 100 spawn locations for Mithril Deposits in Tanaris. I have made a map of the ideal route. It is quite simple though: just make circuits around the edge of the zone. You can skip the northern parts, if you want, as most of the spawns are further in the south.
Mithril and Thorium farming in the Blasted Lands
If you can already mine Thorium, the higher level zones might make more sense for you, as they are more profitable. The Blasted Lands are especially good if you also have Herbalism, as you can pick up Gromsblood on the way, as this zone is one of the zones where this herb grows. Along with this, you will pick up lots of Mithril and some Thorium, if you can farm it already. The Hinterlands can also be acceptable for mithril farming in classic/vanilla, though I won’t provide a map for that, as it is very spread out across the zone.