I've been casually barn-shopping lately, and having an up-to-date website is a biggie for me. It's especially nice if they have current boarding/training/lesson rates listed. I hate making phone calls. On the flip side, outdated price information is worse than no information.
I also like to see photos (of course!) of the facility in all seasons. I like to see/read about what current riders at this barn are doing. Billy got 1st place at a schooling show? Suzzie passed her Level 1 Parelli test? Anne is rodeo queen? Joe is competing in the Olympics? Basically, "Are these people with similar interests who I want to be around with my horse?"
Craigslist is big right now too. I saw a local facility advertise a training special for new boarders on Craigslist. This barn was further away than I'd been searching, but after I saw their special (and link to their excellent website), I seriously considered moving my horse there (30 mins away!).
Monte - 15 year old Paint/TB
Auric - 13 year old Arab