I am not quite sure about what you looking for. Just share some thoughts here:
1) If you want to calculate great circle distance between two points in lat/lon, you could use haversine formula distance. Example in JS:
function Haversine_distance(lat1,lon1,lat2,lon2) {
var R = 6371; // in km
var x1 = lat2 - lat1;
var dLat = x1.toRad();
var x2 = lon2 - lon1;
var dLon = x2.toRad();
var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) *
Math.sin(dLon / 2) * Math.sin(dLon / 2);
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
var d = R * c;
return d*1.0;
};
2) If you need more accurate distance calculation you need some correction factor, since earth is not a perfer sphere. It is always easier to project the locations you have to an appropriate projection and calculate distance there. For instance, project to UTM zones using proj4js, then calculate the distance to reduce the inaccuracy.
3) If you are talking about walking distance in cities, then it is network distance. It is required to have your road network build up first, then calculate from there. Without the road network, giving only point locations will not be enough to calculate the walking distance. Commercial data for road network is available from such as TeleAtlas. Free data can also be found via OpenStreetMap.