06/12/2007 at 11:00 AM EDT
Hugh Dancy and Claire Danes seem to be getting along swimmingly: After attending a spate of events in the last few days, the press-shy couple are planning a scuba-diving vacation.
"I've never scuba-dived, but hopefully, I'm going to, the day after tomorrow," Dancy told PEOPLE Monday at a Cinema Society screening of their film Evening
in New York City. "I'm going on a holiday."
Asked if Danes was going with him on the vacation, Dancy said: "Yes."
But the actor, who just wrapped up a stint in the Tony award-winning play Journey's End
, was coy about their exact destination. When asked if the getaway was to an island, Dancy would only say, "It's not a landlocked country."
He added: "I've never done scuba, but I'm not very good at those holidays where you do absolutely nothing, so I figured I'd learn to swim underwater." (Speaking of tropical getaways, Danes will be honored at the 2007 Maui Film Festival, to be held June 13-17.)
And Danes supports her beau's adventurous side. Backstage at Sunday's Tony Awards in the gift lounge, she requested an Invicta diving watch for Dancy, according to a source.
Dancy and Danes began dating while filming Evening
in Newport, R.I. "We hadn't met before," Dancy said Monday. "It's an amazing place."
Danes recently told PEOPLE
that she and Dancy "just happened upon each other because we were friends" – and Dancy told PEOPLE of the relationship: "I'm having a great time."