Bilbo Baggins is Frodo's cousin and uncle (let's just say that Shire relationships are complicated), and it is from Bilbo that Frodo inherits the Ring of Power. While Bilbo does not appear in The Two Towers directly, his presence pervades the novel in a bunch of ways. Of course, Frodo wouldn't even be in Mordor in the first place if Bilbo hadn't accidentally found the Ring in the Misty Mountains and brought it back to the Shire (see our learning guides on The Hobbit and The Fellowship of the Ring for more on this).
But also, Frodo's whole relationship with Gollum has come about because Bilbo did not kill Gollum back when he had the chance. Bilbo had mercy on Gollum. And as Frodo is deciding whether he should have mercy, too (in Book 4, Chapter 1), he remembers Bilbo's example and decides to spare Gollum's life—a decision that has huge effects on the events of the rest of the The Lord of the Rings series. Gollum also clearly remembers Bilbo: he makes a passing reference to Bilbo's guessing game in The Hobbit in Book 4, Chapter 2. So at least some of Gollum's personal resentment of Frodo comes from his understanding that Bilbo is the filthy thief who deprived Gollum of his Precious almost eighty years before.
The Gaffer is, of course, Sam's excellent father and the gardener at Bag End, Bilbo's old home. He only appears in relation to Sam's many sayings and aphorisms in The Two Towers, but we actually get to see him speak in The Fellowship of the Ring.
The Old Took is the oldest hobbit on record (that is, until Bilbo comes along). He is also the ancestor of the Took family and Pippin's great-great-grandfather. Pippin refers to him as he and Merry are traveling through Fangorn Forest: "[The Forest] reminds me, somehow, of the old room in the Great Place of the Tooks away back in the Smials at Tuckborough: a huge place, where the furniture has never been moved or changed for generations. They say the Old Took lived in it year after year, while he and the room got older and shabbier together—and it has never been changed since he died, a century ago" (3.4.6).
When Théoden first claps his eyes on Merry and Pippin, they are smoking. Pippin launches into an account of Tobold Hornblower, "who first grew the first true pipe-weed in his gardens, about the year 1070 according to our reckoning" (3.8.129). Pippin would keep talking about old Toby and pipe-weed except that Gandalf cuts him off and saves Théoden from a lengthy tale.