Balcony Point is named just for that, a large ledge on the south side of the rock. It can be mistaken for Spire Two from a distance, as it completely obstructs the view from the parking lot. If you look at the beta photo of the Cathedral Spires, the one that I have numbered as 2 is really Balcony Point.
Follow trail #4 from the Cathedral Spires parking lot towards the spires. When the trail branches, the best way is to take the right branch and find the Spire Two-Three gully. Head up this gully (with Rubaiyat Spire at the bottom) and Balcony Point is the second spire from the top of the gully. The spire at the top of the gully is Spire Two.
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Mountain Project's determination of some of the classic, most popular, highest rated routes for Balcony Point:
North Crack 5.6 Trad, 3 pitches, 250 feet
Featured Route For Balcony Point
North Crack 5.6 SD : Custer State Park : ... : Balcony Point
This is a great climb. Start by climbing the first 2 pitches of the east face route on Spire Two. Then, when at the saddle between Spire Two and Balcony Point, climb up to the obvious beautiful splitter crack that goes almost to the summit of Balcony Point. Climb this, the hardest move being pulling through a bulgy crack to the top of the pillar....[more] Browse More Classics in SD