06/03/2011 AT 7:30 PM ET
The duo, first spotted looking cozy right after the Cannes Film Festival, haven’t spent much time apart since then.
Before hopping on a boat ride Thursday, as pictured, they arrived in Venice the night before via private jet. A source confirms to PEOPLE that the stars are staying at the five-star Hotel Cipriani.
After setting sail for the day, Lively, 23, and DiCaprio, 36, cooled off with a frosty treat, an onlooker says, telling PEOPLE, “Their ice creams began to melt and dribble. They were giggling trying to lick the drips up.”
After their icy date, the pair met up with Naomi Campbell and her beau Vladimir Doronin. As for Friday, the new duo has “spent all afternoon by the pool.”