At 12AM Pacific time, there is roughly 585 logged in around Besaid. Your results may vary but here is a way to get an estimate of how many people are in your server at any given time:

Do a search region by region. If results show too many, narrow the search a little such as filtering by online status, location, or level range. For example. Thanalan, Ul'dah alone even, made up at least 1/3 of the population in this search. Numbers may be slightly off as people log in/out, change areas, or even classes. But it's a good way to get an estimate on how many people are in your server on average.