For pasture board,
Is there a shelter so the horse can get out of the rain/wind/snow?
What's the blanketing policy? Are you on your own to change out blankets on those freak days when it's 70 in daytime but 40 at night? Most barns charge $1 a day for blanket changing.
Do they get enough hay & water. All BO's will promise the moon & the stars when you first talk to them on the phone. When you actually go see the place, look around a lot. Check to see that the horse already there have lots of water in their buckets. If it's frozen solid or empty, leave. Look that they have hay or pasture (if you're in a warm climate) to eat. Look for round well fed horses. If you see lots of ribby, skinny ones, again don't waste your time.
Personal preference is size of turnout and how many horses yours will be out with. Just make sure it's what you want for your horse.
Ask why options for grain you have. Most have a few different grains to choose from. Just make sure there's one that will suit your horse's needs and ask how much he will get each feeding.
Ask about the barn rules. Are there any restrictions you would not be happy with. Are they closed on Mondays, can you use your own trainer, do they have any policies about not riding alone, etc. Just ask a zillion question and look around a lot. If you can, talk to some current boarders.
You just have to see your distance...you don't have to like it.