***** NOT A TEACHER *****
You have asked a great question.
Wow! You are right: in theory, we should say, "I prefer to watch TV to to play basketball." Of course, native
speakers simply will not accept " to to." It sounds too weird.
Thus, my books tell me that you have these choices:
I prefer to watch TV rather than play basketball. (No "to")
I prefer to watch TV instead of playing basketball.
I prefer watching TV to playing basketball.
Credit: Dos, Don'ts & Maybes of English Usage by Theodore M. Bernstein with the assistance of Marylea Meyersohn and Bertram Lippman.
Modern American Usage by Wilson Follett (edited and completed by Jacques Barzun).
Student or Learner