Your question is a good one. I'll share my experience with my '08 Patriot:
1) My CVT failed at 110,000 with the humming noise that indicated a bad bearing. I was under the lifetime warranty so replacing it was a no-brainer. My replacement tranny went another 165,000 miles for a total of 275,000, Engine never gave me trouble. My Dad always said if a car had been good to that point, it was worth one major repair.
2) As for whether its worth the repair, I needed a new engine harness at around 200,000 miles. Like you, my Wife and I debated whether it was worth repairing at those miles but our logic was that I'd spent nothing on repairs till then, so why not? In the course of finding and diagnosing the problem I burned out the alternator and wrecked a battery, but other than that I hadn't spent anything out of my pocket so it all came to around $1200. I got another 75,000 trouble-free miles out of it. I figure I got a reliable vehicle for $1200 that lasted me a several more years.
I sold it to a friend and its still on the road.
Following is a bit of advice: "Free advice costs nothing and its worth the price" [Alan Sherman].
Just remember, if/whenever you buy a used vehicle, you're buying someone else's problem. It won't be trouble-free either -- at best its getting closer to the "repair belt," at worst the last owner ran from it! On the other hand I've had a couple experiences with used vehicles where the previous owner over-estimated the problem and I got it fixed on the cheap.
Finally, if you go for the repair, I'd avoid a junkyard tranny. Even if its OK at first, its already well-worn. If it failed in a year (or a month), you'd be in a world of hurt.
A factory rebuilt should take you the distance