IMO the single most important thing is that you like the head. And like, as in you find him/her simpatico, could imagine, other things being equal, having an agreeable chat with him/her in Starbucks. Or can imagine having a meeting with him/her when your unlovely 14yo dc has been caught smoking on a Geography field trip, and coming away from the meeting confident that the situation was being dealt with in a sensible and acceptable way.
Also check out the vibe given off by the support staff (v. important imo). Phone up incognito to ask a slightly dozy question about the entrance procedures, and see whether they give you the 'Oh god, not another stupid parent wasting my valuable time' routine, or whether they actually try to be helpful. Then extrapolate that attitude 5 years down the line to when you want to discuss some kind of problem with them.
Facilities less important, but vibe is all imo. And QPH's tip about whether you can envisage your child ending up like one of the school's 6th-formers. Also the academic range of the school from talking to other parents, there seem to be a lot of people hell-bent on shoehorning their child into the most academically starry establishment possible. I don't get that myself scraping along at the bottom of an academic powerhouse must be a miserable experience, but conversely, so is consistently being top of the class with minimal effort. I would be aiming to find a school where my child could be in the top 30% or so, so that they could feel they were doing well but would still need to make an effort achieve really good results.
We looked at loads of v. popular N. London schools, both state and private. Some were off-puttingly snotty when you phoned up with an innocent enquiry or tried to make it as hard as possible for prospective parents to look round (kind of understandable when you think they have 2000 people applying for 180 places, but still). At others we got the feeling that we weren't just yet another prospective parent and that they would go out of their way to care about the individual. Dd1 passed the exams for all the glitzy N. London grammars as well as the glitzy private schools we applied to, plus a scholarship or two. But the school we actually chose had a completely delightful head, comparable results to the big name selective schools despite a wider intake, and the feeling that they really cared about each girl there. I haven't had a moment's doubt since she started on Sept 5th.
hth