Were they still living with their parents, or did they live somewhere near their shop in Diagon Alley?
They lived in Diagon Alley, above Weasleys' Wizard Wheezes.
Mrs. Weasley tells Harry he'll have Fred and George's room to himself, since they've moved in above their store.
“Bed,’ said an undeceived Mrs Weasley at once. ‘I’ve got Fred and George’s room all ready for you, you’ll have it to yourself.’
‘Why, where are they?’
‘Oh, they’re in Diagon Alley, sleeping in the little flat over their joke shop as they’re so busy,’ said Mrs Weasley. ‘I must say, I didn’t approve at first, but they do seem to have a bit of a flair for business! Come on, dear, your trunk’s already up there.” - Harry Potter and the Half-Blood Prince, Chapter 5 (An Excess of Phlegm)