I would look carefully at any daytrip tour to the Grand Canyon. Most tours from Vegas fall into one of two categories: Extremely rushed trips where you get up before dawn, get a few hours at most to do a quick look around, and then get back very late. The others - including most vegas-based helicopter tours - go to the "west rim" which is part of tribal lands that are not a part of the national park.

If it were me, I would recommend making the drive yourself where you can tour the park at your own pace. A air tour will certainly be nice, and could be a nice addition to your visit, but to me, there really is nothing quite like being able to stand on - and even walk a little ways in from - the edge.

Your LA plan is probably along the lines of what I would do myself, I just want to make sure you were thinking along the same lines, and weren't forgetting about the size and sprawl of the area.