The Forest Gump view is southbound. You will see a number of people standing in the middle of the road. There are 2 or 3 pull offs so you can stop from either direction.
Pay the price to see the real "John Wayne" Monument Valley and take the Jeep ride. One trip is enough.
DO drive through the free Valley of Gods. I go every time I am in the area. The views are better than the John Wayne views and you can stop and hike or even dry camp, but be aware the road is dirt and may not accept a RV.
Free Dry Camp at Muley Point.
Link to Muley Point but be aware that the 4 mile dirt road is VERY washboard but well worth the trip. I use Muley point as a campsite for day trips to Natural Bridges and down the Dugway to see Valley of Gods.
For $5.00 (?) you can dry camp at Goosenecks SP at the foot of the Dugway.