Have you visited the Richard III and Henry VII experiences at Monk Bar and Micklegate Bar? They are useful miniature museums about the Wars of the Roses and staff there may be able to highlight York-specific relevant locations. Micklegate Bar (ie Micklestreet Gatehouse) was the entrance Henry VII used into York when he first arrived as king.

Towton Battlefield is also a short distance (12 miles, ish) from York to the southwest, just south of Tadcaster. Since Towton was one of the largest battles in the Wars of the Roses, it stands to reason it'd be a good place to film a short piece.

If you get really stuck, you could do worse than going to the minster and looking for relevant tombs in the time period, then using those names to look up who followed which cause.

Other than that, do remember that if AJ Pollard's map is to be believed Yorkshire was not the heartland of the Yorkist cause, being in fact largely part of the (Royal) Duchy of Lancaster around the start of the wars in 1461. Instead lands belonging to the Duke of York were particularly concentrated in Wales and Ireland, but it's worth getting a copy of AJ Pollard's short textbook just to see the other places. There is an online version, I can find it if you're interested.