The Eastern Trails Museum is Vinita's local history museum, occupying a historic building in the town centre and offering free admission. The exhibits are genuinely interesting: a recreated post office, general store, printing office, and doctor's office give a sense of what life looked like in the Indian Territory before statehood, and there are solid displays on the Battle of Cabin Creek (one of the few Civil War engagements in what is now northeastern Oklahoma), Native American history of the Cherokee Nation, railroad memorabilia, and Route 66 artifacts.
This is the kind of local museum that rewards a slow look rather than a quick lap. The staff are typically knowledgeable and happy to talk. Allow an hour if you're interested in the region's history.