The 2 hour drive from Phx to Flag is entirely on the highway, and the scenery isn't bad. Probably the better option.
As mentioned, loads of free camping on NF around Tusayan. Just look at a map that shows secondary roads, drive a few miles out into the Junipers, and you're good. This was almost always my favorite option.
Hotels in Tusayan (~5 miles from the rim) are likely a bit cheaper than in the park. However, when I payed money to sleep at the canyon, I always reserved one of the small, cheaper rooms in the El Tovar. It's the oldest hotel and is right by the rim, and the smaller rooms are often cheaper than rooms in the other (generic) hotels. Tip: there are 2 tables in the cocktail lounge with excellent canyon views. Snag one early, order a beverage and their excellent nachos, and enjoy the sunset.