According to http://www.amazon.co.uk/Growing-Pains-PC-Penrose-DVD/dp/B000LC3RVQ/ref=sr_1_1?s=dvd&ie=UTF8&qid=1366113083&sr=1-1&keywords=rosie it's set in "the Yorkshire town of Slagcaster." I bet that pleased the local tourist board.

Am not much good at downloading the pictures but am suprised by the UK members no ones found this lovely little gem of episodes of Rosie on YouTube.. Rosie,, its like a cross between Last of the Summer Wine (as it was written by Roy Clarke) and Heartbeat !! Scarbrough seems a much more gentle place back in 1977-1978.. with lots of Cortina's,Escort's Mini's and Maxi's plodding around.. You might just see the odd "United" Leyland National in the background too.. Love the VP Princess having its clutch crucified!! Enjoy!!
https://www.youtube.com/watch?v=NoAf2IKEHXQ
https://www.youtube.com/watch?v=FS_aVt5RQfU