Olympic cities along with the countries as a whole benefit from hosting the Olympics for the rest of the world. It gives them the whole spotlight of basically every country in the world and of course that equates to a lot of people along with money that is brought into the country.
Hosting the Olympics is a very expensive undertaking and requires a lot of planning and construction. Many cities who host the Olympics do not plan for what to do with the structures and venues after the Olympics are over, and so are left wondering what to do. There are some exceptions, however, such as the allowing some of the structures in Atlanta to be re-purposed for the Atlanta Braves to use. Unfortunately, many of the Olympic venues fall into disrepair and some have been destroyed in wars. The cities may not always win financially, but people will remember for a long time the majesty that the Olympics brought temporarily.
I really enjoyed watching the winter olympics this year. There were many events that I liked. The Russians were really good in virtually ever sport. It was hosted in Moscow the capitol of Russia. They made the most gold medals and really beat up on the USA. They did a real good job.
Usually the host nation of the Olympics takes home gold medals in several of the different categories so I would say the host cities win some and lose some just like every other nation competing in the Olympics, I think judges are impartial to all the athletes and judge by score and ability only.
Since cities are not competing in the Olympics, no. Of course not. And there is no main even to "win" at the Olympics, either. Many host nations do well at the Olympics, but that's typically because they have the most athletes participating. This is due to lower domestic travel costs.