Some Came Running is a Sinatra vehicle that works pretty well. Here to Eternity offers another good Sinatra performance - he got an Oscar for that, if I recall. Frank did a great job in Manchurian Candidate, too, IMO.
Now, if ya wanna a movie that'll make ya laugh at Frank - not his intention at all, I'm sure - ya just gotta see The Pride and The Passion. Great spectacle, improbable plotline (salvaged somewhat by a young Sophia Loren - her script lines weren't all that much, but she had some real costume-strainin' lines of her own
), and essentially pathetic, mis-cast, and indifferently played Sinatra character. Apart from Ms Lauren's uhhhhhh ... "
athleticism", the most fun offered in this movie comes from Frank's attempt to render an accent.