Most countries do not have significant intra-national migration barriers. For instance, in the United States, that has a fairly federal structure of government with much power granted at the local (state) level, but individual states do not have the authority to restrict the entry and exit of US citizens.
However, some countries do have significant intra-national migration barriers. An example is China’s Hukou system, which places restrictions on the mobility of people from rural to urban areas and on the access that migrants have to the privileges that urban residents enjoy.
Some people have also argued that there are de facto (as opposed to de jure) restrictions on labor mobility imposed by various regulatory and zoning policies that artificially push up prices in certain areas, making those areas difficult to afford for people of limited means.