This Mithril Ore farming guide will show you the routes that I use for farming Mithril Ore in Classic WoW. Some of the areas changed in Burning Crusade Classic because some mobs became non-elites, but the farming routes are still the same for both Classic Era and TBC Classic. Level 70 players will just have an easier time farming because you can avoid pulling most mobs.
If you want to farm different ores, please see my other guides:
Copper Ore Tin Ore Iron Ore Thorium Ore
Hinterlands is the best place to farm Mithril simply because most minerals veins in the zone are Mithril Deposits. You will only get a few Iron and very few Thorium.
The red route should be skipped by lower level players because the area is filled with level 62 elites. Lower level players might also want to consider skipping the cave marked with a red circle on the map. (depends on your gear/class)
Tanaris is also a very good place to farm Mithril Ore, but you will have to travel a bit more between Mithril Deposits.
Players below level 60 should skip the 4 caves marked with red circles.