Frodo leaves everything to Sam when he sails over Sea. From "The Grey Havens", Chapter 9 of Book Six:
"But you are my heir: all that I had and might have I leave to you."
The Tale of Years, Appendix B describes how Sam was elected Mayor seven times, and then, in 1482:
Death of Mistress Rose, wife of Master Samwise, on Mid-year's Day. On September 22 Master Samwise rides out from Bag End. He comes to the Tower Hills, and is last seen by Elanor, to whom he gives the Red Book afterwards kept by the Fairbairns. Among them the tradition is handed down from Elanor that Samwise passed the Towers, and went to the Grey Havens, and passed over Sea, last of the Ring-bearers.
And although it isn't made explicit, the family trees in Appendix C show Sam's great-grandson Harding described as "Harding of the Hill", presumably referring to Hobbiton Hill and therefore implying that the family still lives at Bag End, which was under that hill. (Harding was descended from Sam's second child, Frodo: his first, Elanor, married Fastred of Greenholm and together they began a new settlement on the Westmarch, of which they became the Wardens.)
But you should also know that the Sackville-Bagginses are no longer enemies by the end of the book: Lobelia showed great courage in standing up to Sharkey (Saruman)'s gangs of thugs, and is forgiven by everyone including Frodo:
Then there was Lobelia. Poor thing, she looked very old and thin when they rescued her from a dark and narrow cell. She insisted on hobbling out on her own feet, and she had such a welcome, and there was such clapping and cheering when she appeared, leaning on Frodo's arm but still clutching her umbrella, that she was quite touched, and drove away in tears. She had never in her life been popular before. But she was crushed by the news of Lotho's murder, and would not return to Bag End. She gave it back to Frodo, and went to her own people, the Bracegirdles of Hardbottle.
When the poor creature died next spring - she was after all more than a hundred years old - Frodo was surprised and much moved: she had left all that remained of her money and of Lotho's for him to use in helping hobbits made homeless by the troubles. So that feud was ended.
If you haven't yet read The Scouring of the Shire, I do recommend it: for me it's among the best parts of the book.