You can simplify things a little. For the yoyo to be stationary, the sum of the torques around
any point, not just the center, needs to be zero. By considering the point where the yoyo touches the floor, F, W, and N all have zero perpendicular distance from that point. Since there are no forces to counter it, the force from the tension in the string must also have a zero perpendicular distance from that point.
So the qualitative answer, "The angle where the string aims at the point where the yoyo touches the table," would have been equally correct.
Draw the right triangle from the point where the yoyo touches the floor to the yoyo center to the point where the string first touches the axle. Some simple geometry will show that the angle between the string and the floor is the same as the angle from that right triangle at the center of the yoyo, which is arccos r/R.
[ May 08, 2006: Message edited by: Ryan McGuire ]