I Don't have a big problem with blackheads but I did have a couple sorta in the crease of the nose/cheek.
I noticed when I started cleansing my face with castor oil (I apply onto dry skin and work in, then steam off with a wash cloth) these pretty much all lifted out. Castor oil acts like a clay face mask-it draws impurities from your skin. It's very cheap and can be used for lots of things so it might be worth a try.
It's slightly more expensive but Origins Clear Improvements charcoal face mask has good reviews for blackhead issues. I use this as well and love it, but I don't really have any blackheads so I can't comment much on it
Origins do tend to give out free samples where I am at least, so it might be worth asking for one if you see a stand somewhere.