'The Bachelor'' s Lauren Says She and Arie Are Headed Home from Their Romantic Eurotrip

The couple are back from their overseas adventure, but they have some explaining to do about all that Instagramming

The Bachelor‘s Arie Luyendyk Jr. and fiancee Lauren Burnham are back to reality after their whirlwind European vacation.

“We’ve had such an amazing time exploring Iceland and Barcelona,” Burnham tells PEOPLE of their adventure abroad, which Luyendyk Jr. referred to as “fleeing the country” after his highly controversial finale episode left fans of the show reeling.

“Although we traveled all around the world on the show, we didn’t really get the experience of traveling together as a couple,” says Burnham. “It’s been fun trying to navigate these places and we’ve made a lot of new memories along the way!”

The newly engaged pair first jetted to Iceland, where they took in the island’s otherworldly natural wonders — and got in a little adrenaline rush courtesy of race car driver Luyendyk Jr.

“We rented a car and drove all over Iceland and I have to say that was one of our favorite parts of the trip. The landscape in Iceland makes you feel like you’re on another planet,” says Burnham.

She adds, “Some other stand out moments from the trip were standing over a waterfall just the two of us in Iceland, Arie racing our tiny, tiny rental car through the snow, and getting blown over by the wind at the black sand beach.”

On their second stop, Burnham and Luyendyk Jr. could be found “scootering around Barcelona, exploring all of Gaudi’s works, eating gelato and having cappuccinos five times a day.”

The reality stars stayed in a two-floor suite at the Iberostar Paseo de Gracia hotel. Luyendyk Jr. gave a tour of their “insane” accommodations on Instagram Live.

But the sweethearts didn’t pack their schedule with tourist activities. “Our morning routine [was] eating breakfast in our hotel room while watching music videos, taking advantage of the breathtaking view from the balcony of our hotel and last night we saw a Flamenco show,” says Burnham.

Having given Bachelor Nation a moment to cool off, they’re now relieved to be heading back to the States. “We are officially tapas-ed out and ready to be home!” she says.

The couple had declared they would be taking a break from social media during their trip, but both posted regular updates to their Instagram accounts documenting their every adventure.

Burnham clears up that they technically abided by their social media detox: “I know our social media ‘break’ has been a topic of conversation,” she explains. “We have just been excited to share our life outside of The Bachelor with everyone since we’ve been having so much fun! The break we mentioned was more directed towards spending time reading comments, not about posting pictures.”

What’s next for the world travelers?

“We’re now on our way home to spend some time with my family,” Burnham reveals. “Then we start the big move to Arizona!”

With reporting by Aili Nahas.