That doesn’t really have to do with the autorouter, it has to do with your component placement. If you put through-hole parts on the top side, you will solder them on the bottom. If you put SMD components on the top, you will solder them on the top.
My guess is you are trying to avoid vias in general because you are making a homemade PCB without through-hole plating. The question you are probably asking is how to avoid vias altogether, except at component pads, where you can use the component lead as a via by soldering top and bottom.
One way to do this is to draw a rectangle on the vRestrict layer that covers your entire board. Eagle will not place any vias in a board area that is covered by vRestrict objects.
The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons