I am based in Miami and I am aware that some areas do not allow drones such as airports or some public areas. Before I purchase a drone, is there somewhere I can access to see restricted areas? Also, are there permits to still fly these in restricted areas?
This is a good reference from DJI people...
Miami-Florida looks like this:
The DJI fly safe map only shows those areas that are block by DJI Go or DJI Go4. These areas are not the same as FAA airspace designations. For the definitive answer on where you can legally fly in the USA you should consider viewing a VFR chart. https://www.faa.gov/air_traffic/flight_info/aeronav/digital_products/vfr/
Furthermore, private (and public) land owners can restrict use of individual on their lands. For example, it is illegal to operate motorized equipment in a Nation Forest Wilderness Area, National Park, and may city parks. While an FAA 107 holder could legally fly over these areas it would be illegal to operate the drone from inside the boundary thereof.
FAA 107 holder could apply for an authorization to fly in a controlled airspace. That authorization would limit the pilot to fly below altitudes listed here: https://faa.maps.arcgis.com/apps/webappviewer/index.html?id=9c2e4406710048e19806ebf6a06754ad
The above link is also a good reference for what areas are off-limits to drone pilots. For example, military bases, missile silos, etc...
For specific rules on recreational flying see this link: https://www.faa.gov/uas/recreational_flyers