Hi Judy,
It depends.
When I was city editor for a large daily, the press was down the hall, maybe 100 yards away from the newsroom. When I was managing editor of a smaller daily, the press was literally on the other side of the wall of my office. I couldn't hang any pictures on that wall as the vibration would knock them off.
Now, as publisher of two weeklies, I don't even have a press! Plenty of small papers, especially weeklies, don't own their own presses. I print at another paper about 40 miles away.
A big cost-savings move these days is "clustering" where a company buys multiple papers relatively close together geographically. It then buys one central press (and other operations often), and all the papers print at the one press, instead of having several presses (presses are very very expensive).
Our company owns 23 newspapers; weeklies, semi-weeklies and dailies. It also owns two press operations. All but 6 papers print at those two press operations.
Clay