As others have noted, the main reason why Atlanta isn't in quite the same league as NYC and Chicago is population and population density. The city's population is a very modest 472,522 (per 2015 estimates/Wikipedia). Moreover, density is only 3,360/sq mile. That falls well short of other U.S. cities of similar size, such as Boston (13,903/sq mi), Washington, DC (11,158/sq mi), and Seattle (8,398/sq mi).
Now if the Atlanta metropolitan region is compared to that of NYC, LA, and Chicago, and their respective regions, the difference narrows somewhat. Still, to a large extent, it comes down to population size and density.
Greater population and greater density in cities generally leads to differentiation in neighborhoods, ethnic enclaves, more variety of goods and services offered, more amenities for the populace, which, in turn, tends to attract a tourist trade. Densely packed cities with large populations also tend to create that special "it" that draws people to them whether to live and work or to visit. A good example is Hong Kong, which owes its vibrancy to its dense-packed multitudes. People often want to visit for that reason alone.
By many standards, Atlanta isn't a world-class city, despite hosting the Olympics in 1996 and being the location of one of the world's principal airport hubs. Neither are most similarly sized U.S. cities, such as Portland, Minneapolis, Kansas City, Milwaukee, Baltimore or Indianapolis. It could be argued there are only four world-class cities in the United States: NYC, Los Angeles, Chicago, and Washington, DC (because it's the center of government). Others that may or may not be deemed worthy include San Francisco, Houston, Boston and Seattle. What do all these cities have in common? With the exception of LA and Houston, all have good population densities. And LA and Houston, despite their low density, possess very significant populations. Atlanta has neither the population nor the density.
One measure today of a world city is a population greater than one million. There's other factors, of course, but the million number is a good yardstick. San Francisco and Seattle are on track to cross the threshold by 2030 or 2040. Boston, Washington, DC, and Portland are steadily growing as well, but it will take a concerted push if any of the three is to reach a million by 2060. Atlanta first needs to cross 500,000.