How do you think your wife will deal with the Grand Canyon? Are her fears mostly while driving, or will the cliffs of the canyon give her problems, even from a safe distance back? If you are concerned, another option might be Zion Canyon rather than the GC. At Zion, you're at the bottom of the canyon looking up. Different type of experience but good for those with acrophobia.
Grand Teton is another good park to visit, as you're looking up at the mountains, rather than driving in them.
While some here are advocating the Mountain Directory, it will only tell you about grades, not whether there's exposure on the side of the road. I know of roads that don't have a very steep grade, but it's 1000' down if you head over the edge. Sometimes street view on Google Earth can be your friend.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)