The Binny Craig is a medium-sized volcanic plug in the Bathgate Hills East of Cairnpapple, North-west of Uphall and South-east of Ochiltree Castle. This Click here for a location map provided by StreetMap.

The Binny Craig from the South-east
According to WJ Watson, "binny" derives from Gàidhlig binneach, "peaked place".[1] The placename element appears in various forms in the area, including Craig Binning, Binnyside Strips, West Binny and Binny House.

The Binny Craig's Summit, Looking South-west
The Binny Craig is one of the highest points between Cairnpapple and Arthur's Seat, affording clear views across the Forth to the North, out to the Pentlands in the South, and Arthur's Seat in the East.

The Binny Craig's Summit, Looking West Towards Cairnpapple
As such, it is highly likely that it was used as a beacon-point in the medieval period (something which CANMORE suggests), but it is also likely that it would have been used in ancient times for bonfires marking the pagan Celtic festivals such as Beltane.
Very little archaeology has been recovered from the Binny Craig, but a small claystone cup or lamp with Iron Age decoration was found there dating, perhaps from around the first century AD, and now in NMS.
However, just to the South-west of the Craig a series of rig and furrow markings are clearly visible from above:

Rig and Furrow Markings, South-west of the Binny Craig
Rig and furrow markings are signs of cultivation, but dating them is very difficult, since such agricultural techniques first developed in the Bronze Age and were still in use well into the medieval period and beyond. It is likely that much of the area was covered in these markings, but the modern farmland around this small surviving pocket has been improved in recent times, obliterating any trace of them.
footnotes
[1] WJ Watson, Celtic Place-Names of Scotland (Edinburgh: 1926), p.146.