I love the idea of the Olympics, but from what I have read and seen, it seems like a lot more ticks in the "Cons" column than the "Pros" for cities hosting the Olympics.
The problem starts with the bidding process. Getting to host the games is an Olympic event in itself - a marathon that starts ten years before the opening ceremonies.Cities form local organizing committees that first compete nationally to become their country's candidate, then internationally to be chosen as host. At each stage, they must convince the selection committee that the city will orchestrate the most effective, elaborate, safe, and convenient athletic blowout of the myriad competitors. As the bidding proceeds, the plans become more and more detailed, spectacular, and expensive.
If the process were rational, each local organizing committee would have a notion of how much their city stood to benefit financially from the games and would cap their bid below that dollar figure. Since the Olympics are likely to generate roughly similar amounts of business activity in any given city, the competition among would-be hosts would drive all of their proposals up to the limit, and whichever town was chosen would reap close to zero net benefit from the event.
Local committees, however, invariably are motivated and run by private business interests which individually stand to gain from the massive construction associated with the events. These interests include construction companies, construction unions, architectural firms, investment bankers, and lawyers, among others. They come together to form a coalition and bring politicians on board.
The result is what economists call a principal/agent problem. The city (principal) is not properly represented by the local organizing committee (agent). The committee that nominally represents the city really represents itself and bids according to its sense of the private benefit (of its members) versus the private cost, rather than the city's public benefit versus public cost.
Since the private cost is diminutive and the private gain extraordinary, the local organizing committees, on behalf of the cities, are bound to overbid, wiping out any modest, potential economic gains.
Meanwhile, during the bidding process cities spend tens of millions of dollars to win the hosting competition. Chicago spent a reported $100 million in its losing campaign to host the 2016 summer games.