From Grand Canyon National Park, take the 64 and start driving toward Monument Valley ! On this road, you'll be able to enjoy many landscapes including the Grand Canyon from different angles, it's beautiful. The drive should take you around 3 hours.
Spend a nice afternoon inside the park, where you can take the Scenic Drive and admire nature's beauty or you can go horseback riding ! For more info on Monument Valley, don't hesitate to go check my future posts about it.
Once you're done visiting the park and want to find a place to stay for the night, go to the Valley of the Gods. It looks as beautiful as Monument Valley and you can drive a loop that will take you around an hour or an hour and a half. You can camp inside the Valley of the Gods as it is BLM Land and it's actually free, just make sure you leave no trace.