Landing for most categories of privately operated light aircraft is free.
There is a very basic FBO in SDQ who can help over there as you are a long way from the main airport terminal.
There may be charges for passengers or parking depending whether you are at Las Americas or Higuero and how long you stay.
All fees for GA are very reasonable in the DR and vary from airport to airport depending on the airport operator.
Punta Cana is free for GA but avoid the FBO which is expensive.