...I think 
"Run Slient, Run Deep" is an obvious possibility for a story involving the Romulans...
		
 
		
	 
Well, 
TOS:Balance of Terror borrowed a lot from the film 
The Enemy Below, which like 
Run Silent, Run Deep was also a submarine film.
 
I would like to have seen Star Trek do a film that was more of a character study or one that was heavy on intrigue rather than one that is action-heavy. I think the James Garner film 
36 Hours would have made a great TOS episode, but TNG already used that one (
TNG: Future Imperfect)
 
I would love to have seen Star Trek do 
Apocalypse Now (or their version of the original book/novella on which that film was based -- 
Heart of Darkness by Joseph Conrad).
 
Star Trek did do something like 
Apocalypse Now/Heart of Darkness a couple of times: 
The Omega Glory (the Ron Tracey Charcter was something like Col. Kurtz) and 
Patterns of Force (with John Gill being similar to Kurtz), but neither of these characters became the demi-god that Kurtz believed he was in film 
Apocalypse Now or the story 
Heart of Darkness.
 
 
Another great character-study film for TOS to do would have been 
The Bridge on the River Kwai. Kirk and Spock would go on a secret mission behind enemy lines to stop a Col. Nicholson-type character -- a legendary Starfleet Captain who has been a prisoner of the Romulans -- from building something (a weapon?) for the Romulans. Of course at the end, the Col. Nicholson-type character comes to his senses and realizes his folly in helping the Romulans, then sacrifices himself to help Kirk and Spock destroy the weapon he has helped create -- Just like Alec Guinness did in the role of Col. Nicholson in the film.