Context would be good, but Have you got something better to do sounds better.
Person 1: I want to go to the movies
Person 2: I don't want to go to the movies.
Person 1: Do you have something better to do?
Example conversation 2:
Person 1: I don't want to be here. [movie theater]
Person 2: Do you have something better to do?
Don't= Do not
In spoken english people usually say don't instead of do not.