There are a couple of places to climb near Newtyle.
Ley Quarry near Pitcur
Climbs: 30 – Rocktype: Sandstone (hard) – Altitude: 100m a.s.l – Faces: South
Very sheltered and sunny aspect with climbing on mainly vertical quarried walls. Most routes start from ledge above deep pool. Takes no seepage so year-round climbing possible. Some reasonable bouldering on short walls at entrance, though a little sandy.
Balmashanner Quarry near Forfar. Red Craig in Glen Clova as well.
UK Climbing is a good source of information on the local crags.
If you are looking for Newtyle Quarry then you need to drive to Birnam near Dunkeld.