As I was worried about if the class goes out of scope and I haven't deleted map. Then, wouldn't that cause a memory leak.
You're right - you should delete map exactly as your code does. But, you should also make your object non-copyable (derive from boost or C++11 noncopyable base classes, or add a private declaration (with no definition/implementation) of the operator= copy assignment and copy constructor. Otherwise, if you (deliberately or accidentally or incidentally - e.g. when storing your object in a container that sometimes copies it around, such as a std::vector) copy your object, then the first copy destructored will delete the map, any other copy that tries to use it will likely crash, and any other copy's destructor that also tries to delete it will also have undefined behaviour.
Do I have to manually call to delete map.
Yes, in your code you do.
A better alternative is to use a smart pointer whose own destructor will delete the pointed-to object.
As I get crash if I call delete in the constructor in my program.
Well, if you call delete after the new, then the constructor won't crash, but you wouldn't have a map object to use after the constructor returns, and if you then try to delete it again in the destructor the you get undefined behaviour which may well manifest as a crash.
If you want to delete the map earlier than the destructor sometimes, you can set the pointer to NULL so that a future delete will do nothing safely. You should then check for NULL before trying to use the map.
Like I could add a method to Level called say destroy map where I delete map. But, was wondering why I can't add delete into the destructor.
As above, you can have destroy_map, but it must coordinate with the destructor.
When there's no compelling reason to do otherwise, it's better to make the map member data, not storing it by reference. When a pointer is useful, use a smart pointer if at all possible. If you want to implement explicit manual memory management, be wary of the issues above.