Since obviously making different countries host it every four years is a diplomatic, economic and socially destructive cluster fuck, I have an idea:

We hold it in Greece. As well as being the birthplace of the games, it also has a load of handy sporting facilities waiting to be used, and is in need of an influx of tourism and that. Also, the weather is good.

Each four years, nations would bid not to host it, but to be the guest of honour, which would allow you to do shit like pick the mascot, curate the opening and closing ceremony, have the torch parade, and generally use it as a nice advert for yourself.

So we still get the Olympics, but no one has to be displaced, slaves don't have to build stadiums, the infrastructure could be continuously improved, the chance of tropical disease is slim to none, countries won't bankrupt themselves over it, etc etc. The only issue might be that some countries might complain about the time difference, but places like America show half of it on delay anyway.

It's perfect. We can ban horse dancing while we're at it.