Luke Skywalker and Marty McFly are often popular choices. Luke's heroism and Jedi powers combined with Marty's relatable and adventurous nature can make for great stories. Another popular combo is Darth Vader and Doc Brown. The contrast between the dark, powerful Sith Lord and the eccentric inventor can create a lot of drama and humor in a fanfiction.
Princess Leia and Lorraine Baines McFly. Princess Leia's strong leadership and political acumen could be an interesting contrast to Lorraine's more domesticated yet still feisty personality. And Han Solo and Biff Tannen is also a somewhat unexpected but interesting crossover. Han's roguish charm against Biff's bully - like behavior could lead to some exciting confrontations in a fanfiction story.
Yoda and Doc Brown. Yoda's wisdom of the Force and Doc's scientific knowledge are two very different forms of intelligence. A fanfiction could explore how they might interact and learn from each other. Maybe Yoda tries to understand Doc's time - travel technology through the Force, or Doc tries to explain the scientific principles behind it to Yoda in a way that Yoda can relate to.