That would honestly depend on what it was erupting. Hot lava and the heaviest projectiles wouldn’t go far from the original site, so that’s only damaging to the immediate area - which has survived eruptions before and will in the future. What would be more damaging to our society would be the gases and ashes that it’d spew. That can travel for miles upon miles upon miles before settling down.
For a good example of why that’d be dangerous to those in the miles around Yellowstone, look at what happened at Pompeii when Mount Vesuvius erupted. Those ash molds of the people who lived there happened because Vesuvius was a huge volcano that spewed ash for miles around, and gave off a ton of heat that caused people to die without overheating the bodies. It’s unlikely this kind of event would happen again, but that’s one reason ash should be feared.
Although dramatic and dangerous, most eruptions in Yellowstone would not be catastrophic. It is actually the spewing out of volcanic dust that would be more lethal than the flow of lava. The widespread and perhaps several inches deep of ash would ruin agricultural land for many miles around and also clog rivers.
Scientists don't expect an eruption for many thousands of years but there is always the potential for one that would devastate the Earth, and not just the vast acres of Yellowstone Park. However, because this has not happened for more than a million years, scientists are not expecting such an event.