The Dictionary of the Scots Language:
DSL - SND1 BRAE, Bray(e), Brea, n.1 Sc. and n.Eng. dial., though occurring in recent literary Eng. [bre:]
1. The brow of a hill. Gen.Sc. [...]
2. A hill or hillside; the high ground adjoining a river bank. Gen.Sc. [...]
3. A road which has a steep gradient. Also used fig. Often found in the names of streets, cf. Windmill Brae, Aberdeen, Bouly Brae, Arbroath. The Lth. quot. below might equally well come under section 2. [...]
4. Upland, mountainous district, often occurring in the name of the district, e.g. Braemar, the Braes o’ Balquhidder. Often in pl.