In my opinion, if a bike is in good condition and can be restored to original condition, and if you have the patience to make it happen, then that is the way to go.
However, if you want your girlfriend to experience the best that cycling has to offer, then upgrade it to more modern components. One thing to consider though is the value of the frame versus the value of the components. Is the frame worth saving or would it be better to just get her a new bike? If the bike was left outdoors, you really need to check the inside of the frame for corrosion, especially in the bottom bracket.
Also, what type of material is the frame made of? If memory serves me, I beleive that Schwinn frames of that time were all steel, and many were high tensile steel. If this frame is high tensile steel, or Hi-Ten, it probably is not worth upgrading. Or if it does not fit your girlfriend anymore, such as if it was her childhood bike, then you should look into getting a better bike that fits her rather than upgrading that one.
These are just a few things to consider. There are others and I am sure that someone else will point out any that I may have missed.
