The best thing you can do is talk to the other boarders. They will give you the inside scoop on how the facility is ran.
Other than that, look at the hay for quality, look at the turn out pastures, the stalls. Ask what is included in boarding. Does it include hay and grain? Do they charge to blanket your horse or take it to the turn out pasture or to hold the horse for the farrier or vet?
Do they allow you to bring your own trainer to the barn? What are the barn hours?
How do they handle vet emergencies? How do they handle injuries/illnesses? Do they turn horses out together or separately?
Do they have limits on riding style (some barns don't allow jumping because of the extra insurance it takes).