There is a $27,000-a-year private school a block away, along with nearby parks filled with playing children and condos with sky-high rents and river views.

But none of that has stopped the city from packing some of the most violent sex offenders into a reviled men’s shelter on East 30th Street that was home to the fiend busted for allegedly raping a woman at a local bar.

Rodney Stover’s housemates at the filthy Bellevue Men’s Shelter included a group of 13 convicted pedophiles, rapists and other sex offenders who are free to wander the neighborhood unchecked, records show.

The pricey Churchill School for learning-disabled children in grades K through 12 is one of six schools within a five-block radius.

“I always see these men drinking alcohol and smoking and sleeping on the park benches. It’s an infestation,” local resident Erika Halcin, 36, said Thursday as she watched her two young kids at a playground adjacent to the Churchill School at 29th Street and Second Avenue.

“I pray to God they close that shelter,” she added. “They are so nasty and they scare all the children. I don’t want to think about what might happen to one of these kids.”

The shelter residents include three convicted rapists and four pedophiles whose victims were boys and girls as young as 6, state records show.

Stover, 48, was arrested Wednesday and a judge on Thursday ordered him held without bail for allegedly pushing his way into a restroom stall at the Turnmill bar on East 27th Street and raping a 23-year-old woman. He allegedly attacked the woman 10 minutes before his 8 p.m. curfew Saturday.

Following his February release from prison after he served nearly 20 years in New York and Pennsylvania facilities, Stover landed at the 850-man shelter at 30th Street and First Avenue.

It houses more than twice as many sex fiends as the Charles Gay Family Center on isolated Wards Island, where six registered sex offenders reside.

And Manhattan’s third city-run shelter, the Life Family Shelter behind One Police Plaza — an area teeming with cops — has just one sex offender.

Even Bellevue’s own residents say it’s a dumping ground for violent ­perverts and crooks.

“This is a f–ked-up building,” one older resident, who asked that his name not be used, said Thursday.

“We got crackheads, killers and all kinds of convicts in here.”

Said a maintenance worker: “The guys who live in here come from hard times. They have had a hard life. A lot of what these guys know is just how to do time in a penitentiary.”

He added, “I don’t make eye contact with these men.”

Few residents recognized Stover when shown his picture Thursday by a Post reporter.

“He kept his head down and didn’t talk to nobody,” said one resident, who added, “It’s a shame that it takes a woman getting raped to get any ­acknowledgment of the shelter.

“He’s one of a thousand guys with problems at this shelter,” he said.

Department of Homeless Services spokeswoman Ishanee Parikh said her office could not confirm the addresses of Bellevue’s 13 registered offenders.

If any have moved, even to another shelter in the city system, DHS would not alert the sex-offender registry.

“By law it’s the individual who is supposed to alert the registry,” Parikh said.

Additional reporting by Kirstan Conley