Standardizing Data for Neural Networks
You can distinguish between the following types of data (source, see Level of measurement for something similar):


Nominal: You can't calculate with them. They only support checks for identity, e.g. names.
Ordinal: You can order them, but not compare the distance. Examples are grades or sizes for cloths.
Interval scaled: Additionally to identity checks and ordering it supports addition. Examples are temperature in °C / °F
Ratio scaled: They support multiplication in addition to the ones before. Examples are mass and length.


For neural networks, ratio scaled feature make most sense. You can sometimes change your view on things to get it, but most of the time you cannot simply transform an ordinal scaled feature to be ratio scaled.

Two tricks for your example come to my mind:


1-hot encoding: Instead of using one number for the country (e.g. 1 for Australia, 2 for Austria, 3 for France, 4 for Germany, ...) you should use a 1-hot encoding (e.g. one bit per country, the bit is only set if it is this country). I am pretty sure this will work much better, although your feature vector will get much bigger. (Attention: Depending on how much data you have, you might suffer from overfitting. You could also partition your dataset according to this feature. So, for example, you might have a lot of data for the US, for France and Germany. But you only have a little data for african countries. Then you could simply have one bit for each of US, France, Germany and complete Africa)
Latitude / Longitude: Instead of using the citys directly, you can use the citys coordinate. This makes your feature even more meaningful and you have two floats for it which are ratio scaled.


You might also think about transforming the country to something more meaningful for your problem (e.g. membership in an organization like OECD).

You could also combine different classifiers. So you could use the "bad scaled features" for a decision tree and feed the result into a NN.