Yelp certainly isn’t all that forth-coming with their advertising program and associated costs.
A page on Yelp.com states, “Yelp Local business advertising packages typically range from $300 to $2,200 per month, depending on how aggressively you want to attract customers.” 
There are no further details given. One must contact them to learn more. It begs one to wonder what they are hiding.
Pay per click platforms such as Google Adwords, BingAd, Facebook PPC, and LinkedIn pay per click do not have any problem divulging estimate costs prior to signing up. In fact, they have tools to let you pre-select your audience filters. During this process, you can view your cost per click or cost per thousand impression (CPM), depend on the advertising model you prefer.
Nearly two years ago, an article by venturebeat.com claims that advertising on Yelp can cost a business 1,000 times the standard CPM. This is for local ads, mind you. Meaning, small businesses are charged this insane rate, which is largely unsustainable.
According to the article, an ad on Yelp could cost you around $600 CPM and the destination page is not your website. Conversely, an ad on a media buy campaign can cost you $10 CMP and the destination page would be your website. With the Yelp example, your visitors are landing on a page that you don’t fully control. While in the latter, your visitors are landing on a page that you do control.
A post on SearchEngineWatch  announced that Yelp is offering a new CPC (Cost Per Click) advertising program. According to a Yelp Representative, you can start advertising with them for as little as $125. There are initial fees (enhanced profile), contract terms, and early termination feeds.
So once again, be cautious on what you sign up for with Yelp advertising.
The good news is that you don’t have to pay Yelp in order to have your business listed with them. You simply have to claim your business listing. Once you do that, you can view stats about your traffic.
If you do have regular traffic going to your Yelp listing, it’s a good indication that you do have a business that people are looking for. It’s at this point you should consider sending that traffic to your own website instead of letting Yelp have it.