BJR123 - Although it may not feel like it at first, the shuttles inside the park are a real good thing. We'd sometimes walk the rim trail between stops. Those can create great spots to stop and soak things in.
I'd agree that lunch at El Tovar would be a neat option. I'd also suggest packing a cooler daily that you can leave in your vehicle and visit as needed. Having cool beverages and snacks of your choosing available takes some stress out of the visit.
Be sure to drink plenty of water while there. During mornings or evenings you may come across deer that are pretty acclimated to tourists. Take photos, but don't get too close.
You should be able to get a current park newspaper off the NPS.gov website to see what seasonal issues they've highlighted. Right now you may be able to see smoke from fires near the North Rim that are just being "managed" instead of being aggressively fought.