Get yourself a "fish." This is a great electrician's tool (inexpensive at most home improvement stores). A fish resembles a really big "tape measure," in that it is basically a retractable strip of metal encased between plastic or metal sides. The retractable metal is narrow and very rigid; it is run down or up through the wall (behind the dry wall and in between the two studs). If you have a considerable amount of polyurethane ("foam") between the studs, be sure to get a very rigid fish (which you should be able to "fish" through the foam). You start with two holes. One from which you start feeding the fish through and one from which it emerges (you will have to find the end and "fish" it out with a coat hanger or wire tool). Then you secure the end of the speaker wire to the end of the fish and then you pull the whole thing back through from the point from which you stared. It's pretty easy. Get good measurements so you have a good idea of where the holes will be (this will allow you to make smaller holes, which will be easier to repair).
Note: If you are going from the first floor into the basement, you will have to gain access into the wall on the first floor so that you can drill through the top plat of the stud wall below. If you are going from the first floor into a wall attached to the basement foundation wall (block or poured foundation) you don't want to drill into the top plat, as you will end up within the foundation wall. Check to see how the basement is firred out (1x2 or 2x4 - many basements are firred out with 1x2, which only leaves you about three qaurters of in inch). Measure very accurately!
Note: If you are going from the first floor into the basement, you will have to gain access into the wall on the first floor so that you can drill through the top plat of the stud wall below. If you are going from the first floor into a wall attached to the basement foundation wall (block or poured foundation) you don't want to drill into the top plat, as you will end up within the foundation wall. Check to see how the basement is firred out (1x2 or 2x4 - many basements are firred out with 1x2, which only leaves you about three qaurters of in inch). Measure very accurately!