Squaw Valley, California hosted the 1960 Winter Games, and that might even be less important than Lake Placid. But that was in the old days when the Olympics, and especially the winter games, were much smaller.
Atlanta’s competition for the '96 games were Nashville, San Francisco, and Minneapolis (which was runner up). The Top 5 US cities didn’t bother to bid for it. Atlanta was determined to have the best potential infrastructure to host a games at the time (it also had a pretty good story of arising from the ashes of its racist past).
Winter Games sites, historically, were not necessarily held in big places, but rather in places where winter sports took place. The Winter Games are a very different thing in that they are, obviously, in need of cold weather and mountains, whereas you can hold the Summer Games basically anywhere someone’s willing to spend a lot of money.
So if one looks at a list of Summer Games sites, it’s mostly great cities, usually a country’s greatest city (Seoul, London, Paris, Rome, Mexico City, Tokyo, Moscow, Helsinki, Sydney, and Montreal was Canada’s greatest city at the time, though it isn’t now) or on occasion second-greatest (Los Angeles, Barcelona, arguably Melbourne, and Melbourne and Barcelona are damn close to Sydney and Madrid In importance.) Atlanta, really, is a weird outlier in Olympics history; it is the one host city that is nowhere near being among its country’s greatest cities.
Winter Games locations have mostly been “hey, here’s a place with mountains and snow.” Prior to recently, actually, most Winter Games were NOT in big towns; Sapporo is a big city, but places like Albertville, Lillehammer, Cortina d’Ampezzo and Innsbruck are just geographically appropriate. Squaw Valley isn’t even a town at all. It’s only recently that they’ve had a run of placing the Winter Games in bigger cities.
The other outliers are St. Louis http://https://en.wikipedia.org/wiki/1904_Summer_Olympics, and Los Angeles (which only ranking 5th in population among US cities when it first hosted in 1932)http://https://en.wikipedia.org/wiki/Largest_cities_in_the_United_States_by_population_by_decade#1930. I don’t think its a coincidence that they are all in the United States. There really aren’t very many other countries that are big enough to have multiple cities capable of hosting the summer games.
BTW, the 1904 games were originally awarded to Chicago, but later moved to St. Louis. An description of these games makes for some interesting reading. It was only the 3rd time the Olympics were ever held, and obviously they hadn’t yet figured it all out.