I'm going to suggest that you try Jaws. Yes, the cinematography is out of date, but the mechanical shark was hokey even at the time. The story is pretty solid: small town politics, fear of the unknown, good suspense, and an exciting climax. It's slow by modern standards, of course, but the characters are solid, between the small town sheriff, the small town mayor, the scientist, the fisherman, and the various townspeople it's a good blend. It's more suspense, with a little gore, than actually horror.
Maybe you'll hate it, but at least you'll know.