Given Graphics object, how do I determine the range of coordinates needed to include all of graphics? Basically I need something like what Show doe
You can try adding a recognizable object at a known location and then see where it shows up in the exported version to provide a scale reference. I thought a vector export (SVG or EPS) would be easier to parse, but I think raster is easier after playing around a bit.
For example, add a green rectangle covering the theoretical plot range:
g = Graphics[{Blue, Thickness[1], CapForm["Round"],
Line[{{0, 0}, {1, 1}}], Green, Rectangle[{0, 0}, {1, 1}]}];

im = Rasterize[g, ImageSize -> 360];
xy = Transpose[Position[ImageData[im], {0., 1., 0.}]];
pad = Map[{Min[#1], 360 - Max[#1] } &, xy];
Show[g, ImagePadding -> pad]
The code is basically identifying where all the green pixels are. The padding in this case is {{92, 92}, {92, 92}}, but it need not be symmetrical.