The north rim closes early because of snow so the south rim is where you need to go. Tho I was a north rim promoter for years we did the south rim this year and I have to admit it has better views. Drive the road to the east entrance and stop at the viewpoint pull outs and get out and walk around at each. At the main village walk the the rim trail. If you are very fit then take some of the trails off the rim trail but they can be strenuously steep.
We boondocked for 5 days in the surrounding National Forest. There was plenty of room but we were there early in the season in April. Before the big mobs arrive. Maybe the crowds will diminish by Fall.