Create a plane on the surface of the cylinder - may be a good idea to make it parallel to an existing plane (less work).
Start your hole feature. Set your point (for the hole location) on the surface (automatigly creates the tangency constraint).
Select the point an mate it to the surface. Bam! it's start and should go through the part.
Dimension to the height and ouila! It's A hole!
I think I left an important part out, I am working in an assembly. I did the hole in the part the way you specified. Now when that part is assembled I need it aligned to a specific plane in the assembly. How do I do that? I know I can do it by aligning the part plane to the assembly plane but, it seems like there should be a more simple way of doing.
I am new to Solidworks and the system I was using previously gave me the option to constrain the axis of the hole or the tangent of the hole to a plane.
Hope that makes it a little more clear.
wait....are you CUTTING the hole at the assembly level?
Or are you trying to align a hole that is ALREADY cut in a part to a specific plane?
If the first one, then use a 3D sketch to create the hole wizard hole and make the point coincident to the cylinder surface and the plane. done
If the 2nd one, then do one of 2 things:
1) show the temporary axis, and then make the axis coincident to the plane
2) show the sketch from the hole, then use the point from the hole wizard and make it coincident to the plane.