Are there gun-free communities and towns in America?

The answer to this question really relies on the definition of "community." The Supreme Court decision in DC v. Heller effectively ended the use of legislation to prevent gun ownership or transport within a town or city. State and local governments cannot prohibit the ownership of firearms, nor can they prevent the transportation of firearms, though limits can be placed on the conditions of ownership and transport. States and localities can create certain gun-free zones (such as schools) and can prevent the carrying of a firearm onto certain government properties where safety is a concern.
Communities can be different for one particular reason. The Second Amendment only applies to governmental action. Private entities are free to prohibit the possession of a firearm on their premises. So, large apartment buildings or, potentially, housing developments could prohibit the possession of a firearm through homeowner association rules—though this does not seem to be a very popular undertaking.