Area code 503 primarily covers most of the northwestern portion of Oregon.
This includes major cities such as Portland, Salem, and Eugene, although it's important to note that due to population growth and area code splits, not all of these cities are exclusively within the 503 area code anymore. Specifically, parts of the Portland metro area now also use area code 971, which is an overlay to the 503 area code.
In short, if you're looking at a phone number with area code 503, it's highly likely to be located somewhere in northwestern Oregon.