Another fantastic part of the US where we (Australians) have travelled. Didn't use the railway, but drove the road nearby and can second the view that there is no spectacular scenery en route. Unless you have been there before and are taking the train for the sake of it, I wouldn't stay in Williams or anywhere else but right on the edge of the canyon! We had good basic accommodation in Bright Angel Lodge about 15 steps from the edge at most economical rate. El Tovar is magnificent but pricey. We stayed 3 days and could have stayed longer. As another poster has said, it needs to be experienced over many hours and from lots of different vistas along the considerable length of road, which you may not be able to do without a car. There was a free bus in the peak season which I believe does not run in winter, so you can only see where you can walk to, if you come by train. Try Google Earth to get an idea of the train, road along the edge. accommodation etc. Keep checking down over the edge, we saw several condors on the cliffs below.
Jean