There are several synonyms for the phrase "pull towards" which convey similar meanings. "Attract" implies a sense of drawing towards something, often with a magnetic or charismatic effect. "Entice" suggests a tempting allure or an invitation to come closer. "Lure" connotes a bait or a trap to lure someone in. "Draw" has a more general sense of pulling towards something, without any particular implication of attraction or temptation. Lastly, "bring closer" implies physically moving something towards yourself or someone else. These synonyms help convey the message of drawing towards something in a more nuanced and descriptive manner.