Where can I find an accurate statistic or an estimate for the population in any city around the world?
While I will link the most popular sites for you regarding statistics and/or estimates for the populations of cities around the world, you need to know that different sites offer different projections. Also, many of these sites state that they are projections of what scientific calculations determine the world population to be at specific times (normally by hour or day). The problem with these sites, overall, is that they simply cannot be aware of exact numbers. Also, you need to consider the fact that not all births and deaths are "known." Some smaller countries, namely villages who are essentially "off the map," numbers will not be accurate at all; given they do not speak with those outside of their community.
Therefore, be careful when examining the sites and the information that they are offering. Population is simply something that cannot be exact.
Various websites are available that give the city population. One of sites with elaborate city population statistics is: http://www.citypopulation.de where you can select a continent & and from the continent page the country where you have statistics for population of cities and large towns. The population data is updated when available.
The website also provides various maps and other information regardin countries and regions etc.