I have to say, all this running to see the Taj - one can visit the Taj Mahal at sunrise (my wife and I were second and third in the gate) when it's cool, there are fewer people and the sun is putting on its "golden hour" once it's coming up, not to mention at other hours for different experiences.
But wait, there's more: Mehtab Bagh (and its views of the Taj Mahal, needless to say,) the Agra (red) Fort, Fatehpur Sikri (40 km / 25 mi away) - we also saw Swami Bagh, under construction - interesting to see the techniques that went into constructing the Taj Mahal are still being used - Akhbar's mausoleum, etc.
If you really want to do it up, spend 2 - 3 nights at the Oberoi Amarvilas in iAgra for one of the best and most memorable hotel stays you may ever have. Our balcony had - of course! - fabulous Taj Mahal views.