How about a classic The Princess Bride.
I thought Executive Decision was an excellent thriller/action flick and that virtually unnoticed at the box office.
Best Steven Seagal movie, ever. 
Minority Report is good action/suspense type stuff in a sci-fi setting. It takes a bit of thinking to follow, though…if what he’s looking for is mindless popcorn relaxation, it’s probably not what he needs.
If you want to see your dad’s blood pressure sky rocket, rent all the Steven Segals for a Segalpalooza Shite Fest. He’ll be better or dead in no time.
I second “Executive Decision,” “The Incredibles,” “The Rundown,” “Crimson Tide,” and “Minority Report.” And definitely “True Lies”! One of my favorite action movies. “In the Line of Fire,” with Clint Eastwood as an aging Secret Service agent who wins both the day and Rene Russo (THAT might appeal to your bed-bound dad!) is simply outstanding.
Or how about “Top Gun”? The first “Iron Eagle” wasn’t bad, although the sequels all sucked, I’ve heard. “Twister” has plenty of 'way-cool mayhem and devastation, although Mother Nature and not bad guys are to blame. I would also add the 1989 Gene Hackman/Tommy Lee Jones political/military thriller, “The Package.” Didn’t sell many tickets at the box office, but I really enjoyed it.