Hoda Kotb, Savannah Guthrie and Craig Melvin on the Tokyo Souvenirs They're Getting for Their Kids

Savannah Guthrie/ instagram

In between hanging with America's impressive gymnasts and highlighting Japanese culture, the Today show's hosts are also focused on another important task: securing good gifts.

Hoda Kotb, Craig Melvin and Savannah Guthrie tell PEOPLE that while on the ground in Tokyo for the Summer Olympics, they've been keeping in touch with their loved ones back home and taking souvenir requests.

"My daughter has asked for anything besides a T-shirt or sandals. She's 4," Melvin says with a laugh of daughter Sybil with his wife, Lindsay Czarniak. The 42-year-old — also dad to Delano, 7 — adds, "She was very specific about that."

His co-anchor Kotb — mom to girls Hope Catherine, 2, and 4-year-old Haley Joy with fiancé Joel Schiffman — says her oldest requested cookies, specifically. Luckily, Guthrie has the hook-up: "I have so many cookies [from a nearby convenience store]," she interjects.

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Guthrie, 49, meanwhile has secured "a lot of glittery" things for daughter Vale, 6½, but tells PEOPLE and her co-anchors that she needs a souvenir still for son Charles "Charley" Max, 4, with husband Michael Feldman.

It hasn't been too hard, the morning show journalists say, to keep in touch with their family despite the 13-hour time difference from New York City, where Today normally films.

"It's actually worked out okay," Melvin says. "We're polar opposites. I'm able to talk to my kids right after the show [which films at night in Japan, which is morning in New York]. They're having breakfast. Right after them, I can spend some time talking to my wife and eight hours later, I can do it again. So it's been hard, but thank God for FaceTime."

Melvin says he's been showing off the stunning view of the Tokyo Bay from his room during those FaceTimes and is happy to report it "hasn't gotten old to them in three days."

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"Our kids are so excited," Guthrie agrees. "My kids are wearing their U.S.A. shirts, they're cheering on the teams. They're really thrilled that we're here — they can't believe I'm at the Olympics."

And Guthrie — who has been on the ground in Japan the longest so far — adds, "We're making the time change work. I always tell them, 'I'm sending my sun to you' and 'Catch the moon. It's coming your way.' "

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Kotb is grateful her daughter tucked a few things into her suitcase, including a dress and some cat socks. "You want anything that reminds you of home," she admits.

She notes that longtime Today weather anchor Al Roker, 66, has "had the easiest communication with his kids," as his daughter Leila, 22, is also in Tokyo working on one of NBC's Olympics-related productions.

"She's always wanted to do this," says Roker — an Olympics veteran with 15 under his belt. "She was 3 years old at the Salt Lake Olympics and she really was fascinated by the production runners and she's always wanted to do this."

The opportunity to be up-close-and-personal with world-class athletes is not lost on the group.

"Every single one of them has an incredible story," Guthrie says. "If you took the time to learn their story, there's not anyone who had an easy or an average path to get here. Every single face you see in a cutaway has an extraordinary path. ... And to me, it's so much more than their athletic achievements."

To learn more about Team USA, visit TeamUSA.org. Watch the Tokyo Olympics now on NBC.