Is it illegal to get paid to write positive reviews for their business when I have never been to their business?

Yes, it's an illegal business practice proscribed under unfair competition and false advertising laws.

Are they asking for any confidential information from you, such as your bank account number so that they can wire you the funds? If so, it is likely a fraud to get money from you. Why can they not just have their employees, relatives, friends, etc. do so and not have to pay $20? Are you so famous that a recommendation from you would have any real effect? Since you are posting something on line that you know if false in order to get people to spend money on a produce or service they might not otherwise do so, yes you probably are committing a fraud. You would never be prosecuted for it because it is so small and common,but is your feeling of self worth so low as to sell it for $20?

It is against the Yelp Terms of Service 6 Restrictions A 1 to compensate anyone to write a review or to be compensated to write a review. By violating the Terms of Service, would you be breaking the law? It would surely be a tort against the Yelp company. It might also be fraud. You might also risk your reputation by being paid to write a fraudulent review. If the company wants positive reviews, they should ask their actual customers to write some reviews.