I need to improve my sword. Where on the map can I mine ebony ore, where do I find a pickaxe, and/or which merchant will sell me ebony? I have been to quite a few and none seem to have it.

Thank you

On the top of the Throat of the World there is a mine, as well a a enchanted pickaxe. Another mine for Ebony ore is Redbelly mine, which will have a pickaxe laying around.

A ton of blacksmiths sell ebony. I buy mine from the ones in Whiterun. I have no idea where ebony mines are but pick axes are usually in mines.

Almost all of the blacksmiths sell Ebony Ingots, which is what you need, not Ebony ore. There are some Ebony ore veins around but I can't recall where, I think they're more common above ground then in mines tho. I think there maybe some where you find the Notched Pickaxe, but I can't remember to be sure.

Yes, there is an ebony mine there. The Throat of the World.

The only ebony on the Throat of the World is on the very very very tip top of the peak, where you also find an enchanted pick axe. It was awesome to discover this on my own BTW. You have to make your way along the boulders to get there, the path ends at Paarthurnax.

Gloombound Mine has about 50 ore worth of mining. The Throat of the World does not have a mine, just 2 veins.