Though we're not told specifically where Frodo Gardner lived, there's a reasonable amount of circumstantial evidence pointing to Bag End. First, he was the eldest son and natural heir of Samwise Gamgee, to whom Frodo Baggins had entrusted Bag End before departing from Middle-earth. Second, we know that his family, the Gardners, was considered an important one within the Shire, so would be expected to have a prominent Hobbit-hole as their seat. Finally, Frodo's grandson was known as Harding of the Hill - presumably a reference to Hobbiton Hill - suggesting that Frodo's branch of the family retained an association with Bag End not only in his own time, but through at least two further generations.