I have been thinking about this and I have used some strict criteria: spacious outdoor enclosure with suitable vegetation and proper opportunities for climbing (except perhaps for geladas), spacious indoor enclosure with free choice between enclosures for most of the day (allowing for cleaning etc) and good viewing of both enclosures.
These criteria eliminate many good enclosures which otherwise rate very highly, such as the Living Forest at Regent's Park, which is purely indoors, and both Cotswold's lemur walkthrough and the colobus/De Brazza monkey enclosure at Port Lympne because they have no indoor viewing. It also eliminates some poorer enclosures where the indoor areas are off-show, including the ugly hamadryas baboon rock at Paignton and the macaques at HWP, where the viewing is also very poor as the ground slopes away from the viewer and you are always looking against the light, although the pool is a redeeming feature.
I think Edinburgh has some good primate enclosures, although I haven't been there for several years, so my opinions may be a little out of date: the gibbon cage is very tall and spacious, although that doesn't make for easy viewing; the gelada paddock is very good, although the indoor area is nothing special; the paired enclosures of Living Links used to be very nice although gulogulogulo's latest photos are a disappointment because they show only dead trees in the outdoor areas, but my favourite is the little walk-through just above the flamingos - I remember seeing blue-eyed black lemurs there and also white-faced sakis, but it has held other species too. Although the indoor area is not brilliant, I like it because although it's a walk-through it is quiet and thickly planted, so that the monkeys show themselves well, perhaps because they can retreat out of sight when they wish.
I can't quarrel with Pertinax's choice, which meets all my criteria.
But I think there will soon be a new champion, once the outdoor enclosure is ready, the crested macaque exhibit in the Monsoon Forest at Islands will be better than any other monkey enclosure I have seen in the UK.
Alan