If you could find the family in the 1891 census (I've allowed my subscription to lapse, or I'd have a look myself) and if they're still at the South Terrace address, you could look at the adresses roundabout and hopefully locate it geographically.
I've looked at the c1870 OS map, and see that the main streets are named, but there are plenty of other rows of houses that are not.
Rhyl was a new(ish) town in the late 19C, and still expanding, so it could well be that an area was named Newtown.
Have you tried contacting Rhyl library? They might put you in touch with a local historian. I know that there is at least one very good one, but cannot recall his name.