I agree with the above, and you can also request to view the contract, price sheet, and barn rules prior
to your decision. I always recommend that visitors come and view the condition of the horses and stalls. I also point out that horses should be relaxed and comfortable as stable hands enter their stalls, (that tells you a lot about the care.) Barn hours? Arena availability? Turn-out? Security?
The "social atmosphere" is also important. Your barn should be a "stress free" place, a time for fun with your horse, and a chance to socialize with friends. Try to find a barn with riders that share the same "type" of horse enjoyment.
Enjoy your new horse home!