Safety Not Guaranteed maybe?
Woody Allen’s Sleeper?
How about Being John Malkovich?
Or The Manchurian Candidate? (old or new version)
The Final Countdown?
I dislike most mainstream sci-Fi, BTW.
“The Adventures of Briscoe County, Jr.”? Starts out as a pretty standard Western then ramps up the Sci-Fi.
There’s always Cowboys and Aliens.
I don’t think you should necessarily try to show them the BEST science fiction movie ever, but instead show them one that will draw them in and make them more likely to say “well, maybe this sci fi stuff isn’t so bad after all.” I agree with the suggestion that you should try something cross-genre, and keep it light. Don’t show them a movie that will make it hard for them to figure out what’s going on, like the Matrix. Show them something that takes no effort on their part to watch.
Suggestions:
Total Recall - Schwarzenegger action movie with humorous elements. What’s not to like? It does raise the question of “is this real or an implanted memory,” but not in a way that’s hard to follow.
I, Robot - Will Smith action movie with humorous elements. What’s not to like. 
Edge of Tomorrow - If you think they’d be more amenable to a new movie. It’s a Tom Cruise action movie with humorous elements. What’s not to like? Except for Tom Cruise 
Once they’re a little more open to sci fi, show them something like Robocop, Twelve Monkeys, or Blade Runner.
Also, one method I use when talking to people about science fiction novels when they think that they don’t like sci fi and/or haven’t read any is to point out some books that they might just not think of as science fiction for whatever reason. “Oh, I loved Brave New World…but I never thought of it as sci fi. Yeah, you know, you’re right. It IS science fiction!” So maybe mention some generally popular sci fi movies to the neighbors and see if they bite. I’m sure they liked Back to the Future, because who doesn’t like Back to the Future? Maybe they just don’t think of it as “sci fi.” Yet.
How about Contact?
Tremors (Note that I haven’t seen it, but I’ve read about it.)
Starman (This one I have seen.)
Tremors is a very good movie, but I wouldn’t call it sci-fi. It’s a monster movie.
Frequency - stars Dennis Quaid and Jim Caviezel. A thriller/family drama with a sci-fi plot device. Pretty well done, entertaining, and accessible.
Coherence - a recent low-budget scifi film about a group of friends having a dinner party while a comet is in the night sky. Mysterious things begin to happen. No aliens or monsters or explosions, but very interesting.
Last Night (1998) - Something disastrous is about to happen to Earth, and everybody knows it’s coming. The movie is about how different people are choosing to spend their last hours.
This is what I came into say.
Also Back to the Future 3. They are Sci-Fi and Westerns.