Four hanging loins of lamb, beautifully marbled and weighing 10 pounds each, filled the windows of Akropolis Meat Market in Astoria, Queens, on a recent Saturday afternoon. Inside the long shop, more than 30 kinds of steak, chicken, pork and lamb were on offer behind a glass case, and multiple conversations in a mix of Greek and English made for a lively atmosphere. About a half-dozen butchers worked, all wearing white coats.

Manny Michelakis, a civil engineer from Whitestone, Queens, who was with his teenage son, Jason, chatted with the owner, John Gatzonis, 69, near the cash register. Although Mr. Michelakis’s order was ready, he was in no rush to leave. A Saturday afternoon trip to the store to buy a week’s worth of meat for his family has been a part of his routine for the past 35 years.

“John and the rest of the guys are my friends, so coming here is like a social hour,” Mr. Michelakis said.

Jason chimed in with his own praise: “On the weekends, we have barbecued or rotisserie goat with French fries and salad, which is my favorite.”

Customers continued to stream in throughout the afternoon. Some left empty-handed and disappointed because leg of lamb, the store’s best seller, was sold out. Most, however, lingered while one of the butchers prepped the meat of choice. Every piece of meat at Akropolis is cut to order, and first-time customers quickly discover that rushing in and out is hard to do.

Dina Kyritsis, a customer for more than two decades, waited patiently while Vasilios Gatzonis, the brother-in-law of John, who happens to have the same name, carved a whole baby pig with a sculptorlike focus. Ms. Kyritsis seemed to appreciate the care he took: “Since I like to roast the pork with minimal seasonings, it has to be of great quality, and here, it always is.”

John Gatzonis opened the store with his father, Constantine, nicknamed Gus, in 1975. Gus had immigrated from Athens in 1956. He worked at meat markets for nearly two decades before his dream of having his own butcher shop came to life.

“His philosophy was that people should be able to feed their families high-quality meat without paying a lot of money and buy it in a place where they would get great service,” Mr. Gatzonis said.

The Akropolis is cash only. And while the words “organic” and “grass-fed” are considered symbols of prestige when it comes to meat, Mr. Gatzonis, like his father, believes that flavorful and tender cuts can be had without these labels. The store’s supply generally comes from farms within 500 miles of New York City and from the Hunts Point Cooperative Market in the Bronx.

The elder Mr. Gatzonis died in 1995, but photographs of him, as well as his 70-year-old meat cleaver, all mounted on the walls, still set a welcoming tone. The biggest change may be the diverse customer base.

“At first, only Greeks came here, but we get everybody today,” said Angie Gatzonis, the cashier, who is the sister of John and the wife of Vasilios.

As if on cue, Josip Lacmanovic, an electrician, and his wife, Ruzica, who live in Astoria and are from Croatia, walked in. They were buying short ribs for a traditional Croatian soup with vegetables.

“My standing joke with John and the rest of the guys for the last decade has been whether Croatians or Greeks eat more meat,” Mr. Lacmanovic said. “There may never be a clear answer to that, but I do know that anything I get from Akropolis is going to be excellent.”