'RHONY' 's Erin Lichy Wants Her Kids to Enjoy the 'Rich Culture' NYC Has to Offer (Exclusive)

Erin Lichy tells PEOPLE the foodie family of five loves to explore the city's different cuisines

Erin Lichy is stepping into the Housewives spotlight with her head held high.

The real estate agent, 36, a member of the all-new cast of Bravo's The Real Housewives of New York City, tells PEOPLE that it's been "really fun" taking on the reality TV experience with husband Abraham Lichy and their three kids — sons Elijah, 3, and Levi, 8½, and daughter Layla, 6 — by her side.

"Deciding to film was pretty easy. I had a conversation with my husband and my parents and siblings and all of them were very, very supportive. They thought it would be a great platform to show a slice of our life. I come from a pretty strong Israeli family," Lichy tells PEOPLE.

"My kids are so funny. The first couple of times we filmed, I think it was a little ... it took them a minute to get used to it. Then there would be times where my son would come home and be like, 'Why aren't they micing me up? How come I don't have a mic?' So that was really cute."

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"My son has been telling all his friends like, 'My mom's on Hulu. It's Bravo but you can watch it live with Hulu,' " she laughs. "Obviously, I don't let them watch the show because it's inappropriate for children, with all the sex topics. But he loves it and totally gets it's a show. He wants his own YouTube channel."

"My daughter is 6, so she sees it and is like, 'Oh that's mom,' but I don't think she fully understands yet. And my 3-year-old, he has no idea what's going on, which is why you see him walking around with his pants down."

While Lichy navigates the buzz around the show airing, she's sticking to her guns about the importance of keeping her little ones busy, something she joked about in the show's first episode.

"I've been seeing a couple of comments where people are saying like 'Why does she want to have all these activities for kids? Why does she want her kids to leave her alone?' I love my children, don't get me wrong. That's why I have so many of them. But these kids are active and they need activities. I don't mean in any sort of way that I don't want to hang out with my kids."

This summer, her kids are staying busy with different activities, with the mom of three admitting it was "so hard" to send her oldest to sleepaway camp for the first time.

"Levi is at sleepaway camp, which has honestly been so hard for me. I did not expect how hard it would be," she shares. "He's having the time of his life but when he called about a week ago, I got so choked up. I just miss him and he was like, 'Mom, you're going to be okay.'"

"My other kids are in camp until about 3:00 pm each day. I love to spend summers with them. We go to the pool, we go into town. We're out east for the summer and it's a lot easier than being in the city at times, so we're very much enjoying our summer together."

When the family of five is home in the city, Lichy says they consider themselves "experimenters."

"We're raising our kids in the city, so we like to do different cuisines on the weekends. We took our kids to a dumpling house in Chinatown where they saw the dumpling carts going around for the first time, and they loved it. We love to go out for an Italian night. The restaurants in New York are so exceptionally good and it's such a special part of the rich culture of the city," she shares.

"We like to make experiences part of their upbringing," she continues. "They're so cultured. We love going to the theater and exploring the things that set New Yorkers apart. It's so rich in culture that our kids can really immerse themselves."

Lichy is looking forward to spending the rest of her summer "decompressing and enjoying time with my family.'

We want to really sort of zone out, which I need after this year. We've been so busy with the launch of the show that it's a time where staying put is more relaxing than traveling, though we have been thinking about travel."

As the rest of the season of RHONY rolls out, Lichy hopes people will realize "I'm authentically me."

"I tend to be like that, where I just kind of do things, and I don't really think much before. I'm a yes person," Lichy says. "I didn't really have any preconceived notions, but it's a lot, I'll be honest. The press that's coming out, the comments on social media, it's a lot to share your life. And the other thing is, you don't really realize it when you're filming. You're just living your life."

"I'm not sugarcoating anything. Maybe I should be, but I don't know how to put on — for friends, for the cameras. I just am who I am and I hope they like me for it and appreciate that. I'm a good person and I hope everyone sees my intentions and who I am. I just want to entertain and have fun with this."

And while she's enjoying her "amazing connections" with castmates, she also wants fans to know she's grateful for the series' response so far.

"We obviously were all a little nervous because we were filled very big shoes. The original RHONY women have been beloved for so many years and I love them as a viewer myself," Lichy says. "It was a scary thing to come into an already established show. We didn't know if we were going to get such a response, but I mean, people really get it."

"They know that we're being authentic. They know that those fights were real, like the stuff about cheese-gate and the restaurant they wouldn't go to because, again, who cares where we go? But I just want to say thank you because I really appreciate the outpouring of love. I know I've gotten so many messages and comment and it's been heartwarming. It keeps up going and keeps us excited about what we're doing."

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