With a D3100 we are looking at a dSLR that is about 2 years old, 14 MP, with maximum real ISO of 3200. About the only compact camera that has similar image quality is Sony's Nex-3, with a sensor similar to your Nikon. The current Nex-3 is about $500 and would provide images as good (or maybe better since it has a newer sensor) as the D3100 in a smaller package.
After that the choices get into smaller sensors and image quality will be reduced although in many cases probably not enough to notice. The original post did not mention a price or if the OP is considering a compact interchangeable lens camera or if they want a viewfinder. For ease of use a dSLR on "Auto" is probably as easy to use as any other camera so I would not expect any gains there no matter what they get.
Terms like "dSLR quality, etc." can be misleading since dSLRs cover a wide range from a Rebel T3 to a D800e and beyond, with prices from about $400 to more than $3000. Point & Shoot cameras cover an even wider range, less than $100 to about $3000. Because of this most comparisons to dSLR quality are meaningless unless the cameras in question have a similar sensor and lens. Image quality definition also depends greatly on the photographer, where one person may consider an iPhone to be as good as a D800 *for their purposes* while another would not even consider carrying anything less than full frame with top of the line lenses.
