According to Webster's dictionary, a brae is a hillside especially along a river. It comes from Scottish. I was wondering if there is an accurate synonym for brae in American or British English, a word that describes a steep hill that abuts a river.
Not specifically, no. Merriam-Webster does indeed define brae as a hillside especially along a river (with the note that this meaning is chiefly Scottish). However if you check MW's thesaurus and search for brae, it returns no results. Furthermore, The Free Dictionary doesn't even make the distinction that the hill is by a river; it defines brae thusly:
brae (br) n. Scots
A hillside; a slope.
Furthermore, if you look at the page on which brae appears, it also displays the word hillside, since (according to it) they mean the same thing:
hill•side (ˈhɪlˌsaɪd) n.
the side or slope of a hill.
According to Dictionary.com Riverbank seems to fit the definition with:
the slopes bordering a river
Slope from the same source contains the following two noun usages:
ground that has a natural incline, as the side of a hill.
Usually, slopes. hills, especially foothills or bluffs: the slopes of Mt. Kilimanjaro.