I have a 2004 street map of Darlington. Neither Paradise Row or Park Villas appear in the index.
I have a book called Darlington in the 30s and 40s and it has a photo of Coniscliffe Road (Paradise) methodist church, which it says was "situated in the angle of Grange Road and Paradise Row (now Coniscliffe Road)". It goes on to say that the church was demolished in the 1970s to make way for a office block.
I suppose it's possible that Paradise Row has been absorbed in to Coniscliffe Road and that some of the houses may still exist.
It's been about 25 years since I lived in Darlington (and not in that part) but not far from the "angle" mentioned above there is Park Lane, Park Street and Park Place. I suspect your Park Villas would have been around there somewhere too.
I hope this has been of some help.
Wotty.