extra services that might be of "comfort" for you: such as blanketing/clipping/holding for farrier/vet call/fly mask etc
feed: type of feed/ once or twice a day/are supplements required or does the facility feed them if you bring them in or is there an extra charge for feeding supplements
What horses will yours be turned out with (if applicable)
Who is responsible for injury to your horse
Is there a riding area on premises or will you have to trailer away to ride, Is there trailer parking (if you have a trailer)
Look around for things such as fire extinguisher, emergency plan(s),hay and chemicals stored away from barn, well lit at night, maybe even a phone, a wash rack is also a plus
Also look for negative things such as exposed wires, signs of rodents, unclean water and feed buckets, improper manure storage, signs of sickness in other horses (ask to see other horses shot records, worming scheduals and even vet records) down fencing, rotting wood, trash and debris, often loose dogs can pose a personal issue.
You have to know what you want. If your gut says this place just isnt right follow your gut. Make a list of what you want and dont want and go from there. Also remember many boarding facilities offer full and partial board. Some are also closed one or two days a week to boarders to allow for the owners personal "freedom" It takes a lot of work to find the right place. I am a long time boarder and also work for a large equestraian facility. I know both sides of the fence. I am always as careful looking for a boarding facility as i would be a day care for a child.
I know this was a long reply but boarding a horse is a huge decision. Def not something to be taken lightly. Investigate facilities thoroughly. Leave no stone unturned.