When people meet Tramell Tillman, they expect him to be like Seth Milchick, the cheerfully menacing manager he plays on the Apple TV thriller “Severance.”“After people get to know me, they’ll say, ‘Oh, my God, you’re so nice,’” said Mr. Tillman, 41, who won an Emmy Award for best supporting actor in a drama series last year. “They’re surprised I’m not the scary, authoritative guy we see in ‘Severance.’”Mr. Tillman got the chance to show off that charisma opposite Tom Cruise in “Mission: Impossible — The Final Reckoning” last year, and he made his Broadway debut in the 2019 production of “The Great Society.” This month, he will star as a character named Bill in “Spider-Man: Brand New Day.”He recently spent a Tuesday with The New York Times as he shopped for furniture in Hell’s Kitchen and danced through Chelsea.10:14 a.m.Mr. Tillman spotted a vintage Edison phonograph from the early 1900s in Olde Good Things in Hell’s Kitchen. “Can I touch it?” he asked the shopkeeper. He wound it up, and a tinkling tune began to play.He’s almost exclusively a window shopper, though occasionally something catches his eye. “I’ve come to know that if you don’t look for it, it will find you,” he said. “So I keep an open mind.”10:23 a.m.He loves visiting furniture stores around Manhattan with his best friend, Chris. “We call it our suburban housewife moment,” he said. “I never wanted to be an interior decorator, but I love the imaginative part, just exploring.”10:49 a.m.Some of Mr. Tillman’s first visits to the city’s best-known arts institutions were when he was a cater waiter for private events in the mid-2010s. “They close the exhibits, so you have to sneak a tour,” he said. He had long wanted to visit the Arte Museum, an immersive digital art space that opened in Chelsea last year.He’s a regular in the Chelsea area — drawn, he said, to the “very queer-friendly spaces.” “I spent a lot of time going to the bars, many of which aren’t there anymore,” said Mr. Tillman, who last year became the first Black and first openly gay actor to win an Emmy for best supporting actor in a drama series. “So it’s just nostalgic for me.”11:07 a.m.Standing in the center of the Arte Museum’s waterfall room, the roar of rushing cascades surrounding him, Mr. Tillman looked up at the ceiling with childlike joy. In another room, he touched a field of flowers on a wall, and fireflies erupted. “This is amazing,” he said.11:29 a.m.His favorite, though, was the tornado. “I could stay here all day,” he said, letting the column of air envelop him.12:07 p.m.He reveled in a walk past some of his old favorites at Chelsea Market, including the chicken-and-waffle spot Friedman’s and the soft-serve ice cream place Seed + Mill. But he wanted to try the Mexican seafood of Los Mariscos. “I’m usually a meat guy, but I can’t resist this fish,” he said, squeezing the juice of a lime over a pair of tacos.Mr. Tillman used to dance in front of his Baptist church when he was growing up in Largo, Md., the youngest of five. As a boy, he said, this “was not something that was celebrated.” So now, to not only be known for his dance skills on “Severance,” but to have had them help him win an award is “like a dream,” he said.12:35 p.m.As Mr. Tillman pored over the flavors at L’Arte del Gelato — “I always have pistachio,” he said, “so I need to mix it up” — the cashier eyed him. “I’m sorry, I don’t know who you are,” she said. “Maybe you’re like a basketball player or something?”“You’re funny,” he said, smiling.12:42 p.m.Mr. Tillman is a long-walk enthusiast: the West Side to the East Side, the length of Central Park, Washington Heights down to Battery Park. “It’s nice to be able to shut my brain off a bit and just enjoy New York,” he said.12:51 p.m.“I love to come here and just people-watch,” Mr. Tillman said as he soaked in a gentle breeze blowing off the Hudson River at Little Island, the floating outdoor public park and performing arts space. “It feels like a different part of New York. It’s my getaway when I can’t get away.”1:03 p.m.He’s enjoying a bit of a break between wrapping production on his first movie musical, “Octet,” and preparing to begin shooting Season 3 of “Severance.” But though his projects have tended toward the screen in recent years, he’s a theater kid at heart. “My dream would be to find a way to go back to Broadway,” he said. “I’ve been rebitten by the musical bug.”