If you want to grind spiders (for their keys, infantry helmets(the guild has lots, ask and you shall receive) or relatively high Job XP) there are at least 2 good places to find them:
Enter the mines north of Hurnscald, and go left. Climb up the little walkway then follow the path clockwise all the way up to the upper left part of the map. There's a little room here where Kina and Tezer431 are known to hang out.
The spider spawn rate is pretty good here, and if you kill them all you can go a little to the right and kill a few more spiders and snakes while you wait for the spiders to respawn.
However there's another place close by that has a higher spider spawn rate (I think)
Outside the Hurnscald mines there's a building where you can find Caul the alchemist. Go into the basement and head North, then take the door to the left in the cavern. Here is a small room with a chest that can't be opened (I think...). It's guarded by a large number of spiders, and nothing else. If you go into any of the other nearby rooms without a high vit score you might be killed by a large number of monsters sitting on the entrance though.
These are the best spider farming spots I know of. Anyone have some other favorites?