After vacationing in Australia while the actor filmed Thor: Ragnorak, Swift and Hiddleston spent quality time together in L.A.

By Melody Chiu
August 03, 2016 10:55 AM

Hiddleswift is heating up.

Last week, Tom Hiddleston and Taylor Swift took their love back to L.A. – where the singer has a home – for some rest and relaxation before the actor jetted solo back to Australia to continue shooting Thor: Ragnorak.

“Tom and Taylor seem great,” a source tells PEOPLE exclusively. “They spent quiet nights at Taylor’s home and she seemed very happy that he spent time in L.A. with her.”

While the singer, 26, and the actor, 35, hit their respective gyms and ran errands during the day solo, they reunited for dinner dates, like their romantic meal at Santa Monica steakhouse, Hillstone.

Taylor Swift and Tom Hiddleston

For more on Taylor Swift and Tom Hiddleston’s romance, pick up the latest issue of PEOPLE, on newsstands Friday.

Taylor Swift and Tom Hiddleston

“They were tucked away on the second floor,” a restaurant source tells PEOPLE. “They seemed very happy and held hands at the table. They were very relaxed, polite and very pleasant.”

Since they began dating, the “Shake It Off” singer and the Crimson Peak actor have barely spent any time apart.

“After their long Australia trip, you would think they need some space,” says the source. “But they are the happiest when they are together.”

And though it’s only been six weeks since they were first photographed kissing near her Rhode Island home, the relationship appears to be anything but a fling.

“For such a new relationship, they act very serious,” says the source.