Hi Drop Bear,
As Sancti has already mentioned, it will be Netherwood Road, not Hetherwood Rd. It is made up of municipal houses, a small street with a "diamond" in the centre, it's still there, a few minutes walk from where I live, I know a few people who live there.
Quarryhall Street was demolished to make way for the new Police Station, late 1960s - early 1970s I think. So the street no longer exists.
From 1900 - 1930 there would have been a mixture of 2 and 3 story tenement buildings, with a few cottages in between. It was a short street, running off the main street in the area - Windmillhill St, into Orbiston St (probably called Miller St in those days). No hostel or hospital as far as I know.
In the 1925 Motherwell directory the following are at 18 Quarryhall St -
At 18a are G. FARMER, wagon builder. AGNES BOLTON, widow. THOMAS AITCHISON, steelworker.
At 18b is JAMES LOGAN, painter.
Number 25 Quarryhall St must have been a fairly big tenement (by Motherwell standards). There are 15 householders named (this book is almost like a voters roll).
25a - ARCHIBALD BLAIR.
25a - WILLIAM NICOL, wheelwright.
25b - WILLIAM GILFILLAN, smith.
25b - WILLIAM SHARP, steelworker.
25c - JAMES McKELLAR, miner.
25c - ROBERT GILMOUR, wagon builder.
25d - D. B. FOREMAN, steelworker.
25d - ALEX COLLINS, clerk.
25d - JOHN McFARLANE, miner.
25e - MRS ANNIE HAIR.
25f - ALEXANDER PATON, miner.
25g - THOMAS NEILSON, stocktaker.
25h - MRS JAMES PRENTICE.
25i - JAMES ROEBUCK, plater.
25j - DAVID CAMPBELL, steelworker.
Elmpark Terrace was a large section of Airbles Street, made up of 2-story tenenment buildings, about 36 houses (as we call them in Scotland but apartments really). All the tenements in Airbles St were demolished in the late 1960s.
If you let me know the family name of your ancestor I can check the 1911 and 1922 directories.