I don't know why you'd pose that as a question, but not having been to Portland I did the obvious thing and spent a minute in google maps. You're welcome. It turns out Portland has a steel mill not just nearby, but within its city limits.

At the risk of stating the obvious, the point of my question wasn't to literally determine whether any big cities exist without heavy industry nearby, although that would be sort of interesting if it were the case. The point is that any such city is going to be an exception to the utterly ludicrous statement of the OP, "Because you really don't want heavily polluting industries (oil refineries, chemical plants, steel mills, etc) close to a big city." Big cities have always had this. The people there do not "want" them there any more or less than people in a small town would "want" them there.

Hopefully not too pedantic, but they do have Precision Castparts, which manufactures all sorts of aerospace, wind turbine, and other giant industrial things: https://www.opb.org/article/2022/03/02/court-approves-225-mi...