Start at 1:18:12, or maybe a few seconds off from there. Costner will be riding through the Texas plain, and there'll be the kind of music the credits could roll under, and then he'll enter Fort Griffin, Texas. In the next minute or so, he'll talk to a bartender and meet Doc Holiday, and their dialogue will tell you all you need to know about what happened before.
Properly, you should stop at 2:59 something, when it segues to the older Earp in Alaska. Structurally, the ending isn't great that way, but the Alaska sequence doesn't work for me either. No one's really managed to do a great ending to the Tombstone story.
Why you should watch it: Dennis Quaid as Doc Holiday is fantastic. The bits with the Earp family are generally quite good. Joanna Going is an infinitely better Josie Marcus than Tombstone's Dana Delany. Catherine O'Hara as Allie Earp and Isabella Rossellini as Big Nose Kate are great, and if I'd been in charge, I would've given them more screen time.
What's interesting but wrong about it: It's all from the point of view of Wyatt, so you never get a decent sense of who the bad guys are and what they want. (If I'd been in charge, the cowboy gang would get another scene or two.)
Even skipping the parts that don't contribute to the story, Wyatt Earp just isn't as much fun as Tombstone. Costner deserves the Razzie that he got for his performance (Wyatt Earp needs to be played cold--James Garner probably came closest to getting his tone right), but if you like Tombstone stories, the piece I recommend is worth seeing. If you feel like it when you hit 2:59, watch the end and then the early parts as if they're DVD extras.