If you have tracking a great place is Western Karanas, - the spiderlings are difficult to find because it's a big open zone, but they regularly drop two to five silks each.
If you don't have tracking, Innothule swamp has tons of spiderlings, however, they drop few silks. Similarily, there is a little spider cave in the Field of Bones - lots of spiderlings in small area and easy to kill many in short order, but silks are not real common (they drop some other cool things though. It's a fun little cave and you'll likely have the whole place to yourself).
One last place to mention, there is an area in the Ferrott (I think it is in the NE part of the zone)where spider families reside. You can attack the mama spider and 3 to 5 spiderlings will appear out of no where and attack you. They drop spiderling silks and black spider silk. Also, the merchant NPC's in this zone often have silks for sale.