groupBy.js

const data = [
  {
    name: "Alexandre",
    city: "MG",
    age: "45"
  },
  {
    name: "Ricardo",
    city: "MG",
    age: "32"
  },
   {
    name: "Igor",
    city: "RJ",
    age: "43"
  },
  {
    name: "Sidnei",
    city: "MG",
    age: "32"
  },
  {
    name: "Julio",
    city: "SP",
    age: "30"
  },
  {
    name: "Antonio",
    city: "SP",
    age: "30"
  }
];

const groupedData = data.reduce((grouped, { age, city, name }) => {
  // Agrupa por Cidade
  (city in grouped == false) ? grouped[city] = {} : null;
  // Agrupa por Idade
  (age in grouped[city] == false) ? grouped[city][age] = [] : null;
  // Adiciona o Nome a matriz
  grouped[city][age].push(name) ;
  return grouped;
}, {});


console.log(groupedData);

O dev Matheus Valeriano propos uma solução melhor:

const groupCity = (grouped, city) => ({
...grouped,
[city]: grouped[city] || {}
})

const groupAges = (grouped, city, age, name) => (
{
...(grouped[city] || {}),
[age]: [...(grouped[city][age] || []), name]
}
)

const groupedData = data.reduce((grouped, { age, city, name }) => {
grouped = groupCity(grouped, city)
grouped[city] = groupAges(grouped, city, age, name)
return grouped;
}, {});

console.log(groupedData);