Stuff I looked for (some before going, some while checking out the place)
1. tried to get price over the phone or email first; I didn't want to waste anyone's time if I couldn't afford to board there!
2. cleanliness of the facilities: were the stalls/pens clean, or did they have a day's worth of poop sitting in them? Same with the turn out areas. I also looked at neatness, as in, was there stuff lying around that could hurt a horse? Empty feed sacks blowing in the wind that show they are not concerned about keeping stuff neat?
3. condition of the current horses. This might be a reflection of the individual horse owner's care of her horse, but can also be a reflection of the feeding quantity/quality. If all the horses are in bad condition, there's a problem.
4. I tried to get a look at their hay, both storage conditions and actual quality of the hay.
5. Amenities: is there an arena, and when can you use it? Lots of places say they have an arena you can use whenever you want, but then use it for daily turnout, which limits your usage time. Are there things like cross ties, a wash-rack, a round pen, jumps, etc you could use? One important thing for me was my own tack room; avoids people borrowing your stuff
6. access to trails? This was a big one for me, because I get very bored riding in an arena
7. do they offer lessons, and do they care if you bring in someone else to give lessons/training
8. what are the hours they are open to you coming? lots of places around here close the barn at 6pm, which sucks if you work. I found a place with pretty much unlimited hours (within reason, they don't want you out there at 3am).
9. care of the horses: how often are they fed? are they turned out (where, and how often, for how long)? will they blanket for you if you need it, or is there an additional charge?
10. farrier and vet stuff: do they have both on call? do they schedule vet and farrier days to save on farm-call costs?

That's all I can think of right now...