The Yanille agility dungeon is a dungeon underneath the city of Yanille. It has two entrances: north of the city and an entrance inside the building south of the bank in Yanille which grants 50 thieving xp when picked, requires a lockpick and level 82 Thieving. This dungeon contains various agility obstacles requiring between 40 and 67 Agility to complete and also contains the Sinister chest and many Chaos druids, most notably Salarin the Twisted.
Balancing on ledge repeatedly results in a maximum of 27,900 Agility experience per hour. You stop failing the ledge obstacle in the Yanille Agility Dungeon at level 65. Swinging on the ropeswing results in a maximum of 29,500 Agility experience per hour. This rate would be lower in reality because Chaos druid warriors can reach you on the north ropeswing and are aggressive until level 88 combat. Additionally, at 72 Agility it's possible to fail this obstacle (at a rate of only 1/35 approximately) and at level 77 Agility you stop failing this obstacle, so it's not recommended to train on the ropeswings until failing is very rare or you have 77 Agility.
Note that in comparison to these obstacles the Wilderness agility course has an experience per hour rate of (35,000 +/- 5,000) at level 70 and (42,000 +/- 4,000) at level 91. So the ropeswing has the highest agility experience rate per hour but the Wilderness Agility course has a higher experience rate for all Agility levels (at least over level 70, anyway, though it's predicted to be slow for all levels).