Altium Designer: How to tell the auto router not to place vias too close to other components?
Have you gone to Design-->Rules and set Design Rules-->Electrical-->Clearance-->Clearance? There is a chart there that allows you to tell it how much space you need between different items, whether they be tracks and vias, tracks and components, vias and components, etc. It looks like this:



EDIT: Oops, accidentally drew the box around the track column instead of the SMD pad column, but you get the picture ;)

I am pretty sure these are the rules that the Auto-router looks at. I am fairly new to Altium, however, so I could be wrong. Worth checking, anyway. Good luck!