I can only speak for Alliance trainers.. But in general:
Swords: Stormwind
Axes: Ironforge
Staves: Darnassus
I believe I've seen thrown, daggers, and hand to hand at all three trainers. I'm betting the only place to train gun is in Ironforge. Bows obviously in Darnassus.. I wonder if Stormwind will train bows?
Hope that helps. I'll try to remember to double-check on the ranged and update my post.
Peace
WT