Went through my list and picked several "oldies but goodies"in my opinion; some are very family friendly; some thriller/horror, classics, just plain fun to watch; but don't base whether you watch them on one or two .. very wide variety here... you may hate the first one, but love the second and so on.
39 Steps
And Then There Were None (1945)
Arsenic and Old Lace
Batteries Not Included (Cute Jessica Tandy and Hume Cronyn; not a classic but it's cute and family-friendly)
Billy Jack: Born Losers
Billy Jack
The Trial of Billy Jack
Billy Jack Goes to Washington
(of the Billy Jack movies, the 2nd and 3rd are my
favorites)
Broken Arrow (Jimmy Stewart)
Coma
D.A.R.Y.L. (cute, family movie; somewhat sci fi)
Dante's Peak (Pierce Brosnan, Helen Hunt)
DeathTrap (Christopher Reeves)
Showtime Series: Dexter (okay, not old, but I love it)
Speaking of Dexter, Six Feet Under (HBO series)
Eight Below (sad, based on true story)
Greyfriar's Bobby (2 versions, 2005 and an older 1; both good)
Enemy Mine
Eragon (when I saw previews thought I would hate this; turned out not so bad)
Finder's Fee
Firefly (series) and Serenity (movie)
Flight of the Navigator (fun Disney movie for family)
Frailty
The Guardian
The House of the Long Shadows (Not sure netflix has this but if you can your hands on it; older version is called Seven Keys to Baldpate (i have both)); has Desi Arnaz, Vincent Price, Christopher Lee, Peter Cushing; but if you can get your hands on a copy it's worth it)
The Illusionist
Iron Eagle
The Island (remake of Logan's Run in a sense, also recommended)
The Man From Snowy River
Matchstick Men
The Mummy Collection (Boris Karloff)
North By Northwest
Pandora's Clockl
Phantasm movies (the first one of the scariest movies I've ever seen, the sequels not so good)
Purgatory (western)
Shop Around the Corner
Summer School
Taking Chance
Time After Time (David Warner, Malcolm McDowell)
Wargames
What Dreams May Come
There is a large variety here. I am always looking for older movies that are interesting and entertaining; sometimes the previews of a movie turn me away from it, but when I'm forced or pushed to watch it, I end up liking it, surprisingly so.
I hope you find at least a couple on this list that you haven't seen and enjoy once you see them.