You don't say where you are flying in to or, as has been noted above, when (time of year). I second many of the suggestions above - you won't be able to get to the North Rim this time of year - not sure when it opens, but likely not much before April or May - probably depends upon the snow level on the Kaibab plateau leading in to the Park from the north side. If you are planning the trip for the summer or late spring, the North Rim is, in my opinion, more spectacular than the South with a lot fewer people to boot (and much cooler in the summertime than at the South Rim). There is a classic lodge - the Grand Canyon Lodge - at the North rim which has fantastic views and as of a few years ago, quite good food. The additional advantage of the North Rim is that to get to it you drive near or even through Zion NP, which is quite spectacular in its own right.
Which ever rim you go to - if you and your traveling party are capable, you should hike part way into the canyon - if even for an hour. You don't have to go all the way to the Colorado River (or even close), but it will give you a different impression of the Canyon than simply staring at it from the road overlooks.