I think you might be right about John Bellairs... but it also could be The Treasure of Alpheus Winterborn. The main character, Anthony Monday, wears a red baseball cap, and a tower room features in this book. You can see a copy of the cover with the baseball cap and tower here: http://johnbellairs.wikia.com/wiki/The_Treasure_of_Alpheus_Winterborn

Sounds like it could be a John Bellairs book.  His Johnny Dixon character is friends with an old man.

It's a book about this boy who wears a red baseball cap (that's one of the few key details I remember), he has to get a new one at some point in the book, and he's friends with this old man that lives in a big old house. I don't remember much else other than that he is in some window tower at some point in the book, I believe towards the end. I read the book in 5th grade, I believe it was meant for 5th-8th graders, roughly. Any help would be awesome.

Young adult mystery