With the Smart Dimension function active, hold down your Shift key while selecting the circle. That will place the dimension to the edge (near or far edge, depending on where you click) instead of the center. I've occasionally run into situations where I need to reference two arcs or circles with one dimension, such as a slot length, and holding down Shift would only place the dimension to the edge of one of the arcs and the other one would still go to the center point. When that happens I just accept it, and then change it to Max (see below).
If you already placed the dimension, you don't need to delete it. Just click on it to highlight it and bring up it's PropertyManager, then go to the Leaders tab. Center will be selected by default, but you can change it to either Min or Max, depending on your needs. The screenshot below is from a sketch in a Part, but the same principles work with dimensions in a Drawing.
This assumes that you were referring to placing a dimension with the Smart Dimension function in a Drawing, or in a sketch in a Part or Assembly. If you're using the Measure tool from the Evaluate toolbar and want to measure to the edge of a hole or circle instead of to the center, then click on the Arc/Circle Measurements icon and choose the appropriate setting from the drop-down. Keep in mind that while Center to Center is the default setting, SW will remember your last setting the next time you activate the tool. It won't go back to the default.