Are his movies any good?

He starred in a movie called "Hong Kong" and played an Indiana Jones style character, complete with brown fedora and matching leather jacket!!!

No. Putting politics aside, his movies were crap.

The ONLY movie he made that I really liked, (and most critics agree it was his best performance), was "Kings Row" (1942).
Other people praise "Knute Rockne All American" (1940), but I like good drama and Kings Row was a best selling book about small town scandal and gossip in pre-WWI America.
It also provided him with the title of his autobiography, "The Rest Of Me".
I must confess that if anyone else played his part it would not have made much a difference. The story was just good and casting was second rate.

I’ve heard that “The Winning Team” and “Bedtime for Bozo” are his best.

But really - he was a B-list actor.

The Killers (1964) directed by the great Don Siegel.

I thought about adding a thread kinda like the top 5 or top 3 movies of RR but then I realized that I had never actually watched an entire RR movie. I've watched scenes on YouTube but no movies. Someone who is an actual fan of Reagan should do that. Of course you can always use Google or IMDb to research his "greatest" movies.

Knute Rockne All American, Dark Victory, and This Is the Army are all good and worth watching.

He was a very good supporting actor in feature films, and lead in second features. He had acting talent, humor, charisma, and good looks. The imbeciles who dump on him are suffering from derangement syndrome because he switched from being a liberal to being a conservative, which is simply the natural progression as one grows up. His movies are all worth seeing, and some are outstanding.