Last week it was New York City. Then on Sunday the couple was seen canoodling on a West L.A. tennis court.

Now, E! News has learned, peripatetic lovebirds Kate Hudson and Lance Armstrong have taken their cross-country romance to Santa Barbara county.

Ludson (Lan-Kat?) was spotted having dinner at Lucky's steakhouse in Montecito late Monday night looking as smitten—and laid-back—as ever...

Wearing a white, beachy cover-up over a bikini and no makeup, Hudson drank a martini and draped herself over Lance, who was equally casual in camouflage shorts, black T-shirt and black sneakers.

According to a source, they shared a table with an older couple and spent the night "laughing and talking," with Kate chatting about her family. "She's so comfortable with him," says the eyewitness. "They're so cute together."

A source tells E! News the couple is staying at the ritzy San Ysidro Ranch in Montecito. How ritzy? Rates go up to $6,000 a night. But can you really put a price on (celebrity) love?