You first have to decide how wide the scope of a variable is. If it is used during the lifetime of an object, make it a member. If you need it only in a single function (and functions invoked by it), make it a function-local variable. In your case, I think you could use many member variables: Tmx::Map, Tmx::Tileset, sf::Texture, the container of sf::Sprites. Declare the objects (not pointers) in the Map class definition, then you can use them in all member functions.
And if you really need new, for example because you transfer ownership, consider std::unique_ptr. This is a smart pointer that automatically invokes delete if the object goes out of scope. This technique is also called RAII, you find a lot about it on the internet. It is a very important idiom in C++, because it simplifies code while making it more robust and safer.