At first, I do think the Sochi Olympics increased President Putin's popularity in Russia, but as of late it seems to be plummeting again. Especially with the invasion of the Ukraine and threats all across the board. Putin is a dictator, so hopefully the Russians will oust him sooner than later.
I definitely think that the Winter Olympics in Sochi helped to increase Vladimir Putin's popularity in Russia. It was clear that a lot of people attributed the success of the Russian Olympic's team due to Putin's presence at the games. A lot of Russians also thought that it was a positive thing to see Putin at the games.
There was no way that the Olympics could hurt Putin's popularity in Russia, given how low of an opinion many had of him to start with. So yes, the Olympics made him more popular for a time. His need to bully a neighbor militarily only demonstrates his need to keep opposition in a state of fear.
Hosting the Olympics is not something to be taken lightly. The international community relies on the host country to really play host to the rest of the world. Hotels must be top of the line. The olympic facilities must provide the best equipment on the market. Transportation should be top notch for competitors. Perhaps the most controversial part of the Sochi Olympics was to do with homosexuality that Putin has made very clear where he stands on the issue.
I do not believe the Sochi Olympics increased President Putin's popularity in Russia. The Olympics were mostly marred with discussion of Russia's anti-gay laws and it was sidelined by raising tensions in the Ukraine, which has led to Russia entering that country. The Olympics were overshadowed by these problems and didn't make Putin's image better.