* Price and what the price includes (blanketing/flymasks on and off are often extra) etc.
* Turn out. Are the horses turned out in groups or individually? What kind of fencing do the turnout areas have? How big are the turnout areas and how long are they turned out each day?
* What kind of stall bedding do they use?
* Feeding schedule and feeding program. What kind of feed, who will be feeding, how many times per day, and at what times.
* Indoor/outdoor arena access? Any trails nearby?
* Do the owners live on-site or off-site?
* Barn schedule. What are the barn hours? If lessons are given at the barn what days/times will the arena be free?
* Lesson option. If the barn gives lessons and you're interested in taking them, some barns give you a slight discount for using your own horse or boarding there. It's worth asking about.
* How many boarders does the barn have? This is nice to know ahead of time if you're looking for something specific like a busy barn with lots of people to ride with, etc.
* What kind of riding do the majority of the other folks do? Not necessarily a deal breaker either way but if you're looking to do a certain kind of riding it's sometimes nice to have others around on the same page.
* How long has the barn been in business/how long have the barn owners been in horses? I once boarded at a barn and found out later the owners had only a few years of horse-keeping experience (which became more obvious to me the longer I was there). Had I been smart and asked about that ahead of time I would have saved myself some trouble.
* Farrier and vet info. Some barns have a farrier that will come out and do all the horses on the schedule, same for vets w/shots, teeth floating, etc. This is a bonus because it often saves you at least part of the barn call fee.
* Which vet do they use in case of emergency?

When you go out to look at the place in person you can check out the cleanliness of the facility (stalls, water buckets, etc.), the condition of the horses, their hay storage set up. Also, noting the attitude of the horses can be telling. If the barn is nice and clean and has a bunch of healthy happy horses in it you've probably found a good place. Ask for references if you're really interested and still on the fence, a reputable barn will have no problem providing them.