In these cities, Boston I believe was the first to ban the company, gay marriage is legal. These cities support all their citizens and embrace the LGBT community. Chick-fil-a contributes a portion of their profits to anti-gay organizations, this is all thanks to their wonderful CEO Dan Cathy :gag:. Now these cities that are banning Chick-fil-a would be facilitating more space and more territory for this company to make money to donate to anti-gay organizations. Money they could very well donate towards Education, Hunger, Training programs to get the American Joe working again... So by facilitating Chick-fil-a they would be aiding them in making money that would work against their own laws, act against their own citizens, and in at the end of the day they have contributed a second-handed donation to publicly named hate groups.
This is an article on ABCnews.go.com by Abby Ellin that explains who donates what and to whom.