This is only a good time to visit if you don't mind a big dry cliff, which is still okay with some people. I definitely prefer it with water, though.
I sincerely apologize in advance if you are already familiar with the USGS Real Time data and how to check CFS, but I will include it for anyone else who is curious about knowing when to visit Grand Falls...
Go to this link: http://waterdata.usgs.gov/az/nwis/current/?type=flow
Scroll down to "Little Colorado River Basin", and under that you want to look for "Little Colorado River at Winslow, AZ" and "Little Colorado River at Cameron, AZ." All the way to the right side of the page there should be 3 columns with numbers in them. The center column represents the cubic feet per second. You'll want to check the cubic feet per second for both of those locations.
Today (7/20), it is flowing at 3.9 cfs through Winslow. In order for there to be a good show of water, it should be flowing at several HUNDRED CFS through both Winslow AND Cameron. Sometimes, after storms or snowmelt, Winslow will be flowing well but not yet at Cameron. It should be flowing well at both gauges, since Grand Falls is between the two towns. There's always a chance, especially if it is a slower flood during spring snowmelt, that the high water has made it to Winslow but not quite to the falls.
I don't have too much experience on the topic of floods and can't speak with authority on it, but based off my trips to Grand Falls, watching the USGS Stream Data and talking to others, following what I said above should ensure a successful trip.
In this photoset: http://www.hikearizona.com/photoset.php?ID=7390
the Little Colorado was flowing at approximately 800 cfs in both Cameron and Winslow.