Right now, Vegas has money to pay two people: Jack and Squat.

I'm sure they have a budget to promote the city, but this money goes towards traditional advertising like magazine ads, TV commercials and billboards.  Remember that these are government employees you are talking about.  They aren't going to be that proactive or that creative.  Plus, they don't need to spend money on product placement to get the word out about the city.  Everyone already knows about Vegas.

The TV shows you mentioned were around for many many seasons.  Almost all TV shows that have been around the block has a gambling and/or Vegas episode.  Just like how most "experienced" TV shows have a Christmas and Halloween episode.  Writers need material and they eventually squeeze a Vegas episode in there.

Does the catholic church pay people to say good things about God?  I've seen so many movies that say good things about him.