C#-Code

using System;
using System.Collections.Generic;
using System.Linq;

const double AverageDistance = 111.3;
const double Rad = Math.PI / 180; // 0.01745

Dictionary<string, Location> locations = new()
{
    { "Frankfurt Main", new Location(50.053764, 8.637086) },
    { "Mainz", new Location(50.001231, 8.276251) },
    { "Darmstadt", new Location(49.872775, 8.651177) },
    { "Würzburg", new Location(49.79245, 9.932966) },
    { "Heidelberg", new Location(49.398752, 8.672434) },
    { "Mannheim", new Location(49.489591, 8.467236) },
    { "Stuttgart", new Location(48.778449, 9.180013) },
};

var compare = new Location(49.00689, 8.403653); // Karlsruhe
var radius = 70.0;

locations.Where(x => Distance(x.Value, compare) <= radius).Select(x => new {loc = x.Key, dis = Math.Round(Distance(x.Value, compare),1) })
    .ToList().ForEach(x => Console.WriteLine($"{x.loc}: {x.dis} km"));

static double Distance(Location loc1, Location loc2)
{
    var lat = Math.Cos((loc1.Lat + loc2.Lat) / 2 * Rad); // Verbesserungswert Längenkreise
    var x = AverageDistance * lat * (loc1.Lon - loc2.Lon);
    var y = AverageDistance * (loc1.Lat - loc2.Lat);
    return Math.Sqrt(x * x + y * y);
}

record Location(double Lat, double Lon);

C#-Code

using static System.Console;

static bool distance_less_than_R(Point ref_point, Point city, double radius) =>
    (ref_point.X - city.X) * (ref_point.X - city.X) + 
    (ref_point.Y - city.Y) * (ref_point.Y - city.Y) < radius * radius ? true : false;
    
//test mit 100 zufallsstaedten
Point[] locations = new Point[100];
double xmin = 0.0, ymin = 0.0, xmax = 100.0, ymax = 100.0; //Begrenzungsgebiet in km
System.Random rand = new System.Random();

for (var i = 0; i < locations.Length; i++)  {
    Point p = new Point();
    p.X = xmin + (xmax - xmin) * rand.NextDouble();
    p.Y = ymin + (ymax - ymin) * rand.NextDouble();
    locations[i] = p;
}

double radius = 20.0; //km

for (var i = 0; i < locations.Length; i++)  {    
    Point pref = new Point() { X = locations[i].X, Y = locations[i].Y };
    for (var j = 0; j < locations.Length; j++)  {
        Point city = new Point() { X = locations[j].X, Y = locations[j].Y };
        if (j != i && distance_less_than_R(pref, city, radius))
            WriteLine($"city {j, 2} liegt im {radius} km Umkreise von city {i, 2}");
    }           
}

WriteLine("ready");
ReadKey();

record Point  {
    public double X;
    public double Y;
}

C#-Code

/*
Erstelle eine Funktion, eventuell mit Hilfe einer Datenbank, 
welche über die Parameter Location (Latitude & Longitude) und Radius in Kilometer 
alle Städte in dem Umkreis mit den Koordinaten ausgibt.

Oder eine Liste mit den Koordinaten in diesem Umkreis. 
Somit können dann die Städte in einer GeoDatenbank ermittelt werden. 
*/
//https://www.kompf.de/gps/distcalc.html
//using System;

using static System.Console;

static bool distance_less_than_radius(Point ref_point, Point city, double radius) =>
    (ref_point.X - city.X) * (ref_point.X - city.X) + 
    (ref_point.Y - city.Y) * (ref_point.Y - city.Y) < 
    radius * radius ? 
    true : false;
    
//test mit 100 zufallsstaedten
Point[] locations = new Point[100];
double xmin = 0.0, ymin = 0.0, xmax = 100.0, ymax = 100.0; //Begrenzungsgebiet in km²
System.Random random = new System.Random();

for (var i = 0; i < locations.Length; i++)  {
    Point p = new Point();
    p.X = xmin + (xmax - xmin) * random.NextDouble();
    p.Y = ymin + (ymax - ymin) * random.NextDouble();
    locations[i] = p;
}

double radius = 20.0; //km

for (var i = 0; i < locations.Length; i++)  {    
    Point pref = new Point() { X = locations[i].X, Y = locations[i].Y };
    for (var j = 0; j < locations.Length; j++)  {
        Point city = new Point() { X = locations[j].X, Y = locations[j].Y };
        if (j != i && distance_less_than_radius(pref, city, radius))
            WriteLine($"city {j, 2} liegt im {radius} km Umkreise von city {i, 2}");
    }           
}

WriteLine("ready");
ReadKey();

record Point  {
    public double X;
    public double Y;
}