Paulo
You could fly the 172 Vegas - GCN and overnight there. GCN gets very busy at certain times, but late afternoon arrival and early morning departure (cooler - look at the elevation!) could work.
You can fly yourself over the canyon through the VFR corridors at 11,000' and 11,500' (ask for flight following), but nothing beats actually standing on the rim at dawn IMHO.
I have some info at
http://www.viewing.com/arizona/canyon/canyon.htm
David