definitely quartzite. See the circular/semi-circular fracture patterns on and beneath the surface? That's conchoidal fracturing which you'll see with quartz (and many other minerals as well - conchoids doesn't always = quartz). I'm guessing you found this somewhere there used to be glaciers, looks like it's been rolled around and beat up by glacial transportation.
It looks like a chunk of quartz. If you are looking for agates on the Yellowstone, they will be darker than that. The surface of them, because they are stream rounded will have little fingernail shaped chips, very tiny and they will look cloudy. Sometimes they will have fresh breaks where you can tell for sure that it is agate. I'm jealous, I want to go with you haha! Other piece looks kind of like pet wood, but it's hard to tell from you pic.