Hi Pam, and welcome. Sorry for all the edits... we avoid mentioning specifics, both for your protection, and because WebmasterWorld has such strong ranking power that mentioning some specifics can actually distort Google rankings.
To clarify your first question....
My client wants to get his website to the top of the natural listings for City-1, Oregon. (He is currently at the top for the neighboring community City-2, Oregon)
When you say that your client wants to get his website to the top for his services in City-1, is he willing to sacrifice his rankings for City-2, or does he want to rank for both City-1 and
also for City-2?
Understand that Google is a machine... it most likely doesn't know where the west side of the city is, and
in the organic results, Google doesn't really rank by location... it will rank by word matches. In the Local rankings, it may rank by distance from the city center, or by office address, etc, depending on the type of business. That gets complicated. But let's just take the organic for now.
Oversimplifying a bit....
If the client wanted to rank organically only for [City-1 services], that most likely would be a lot easier than ranking for both [City-1 services] and [City-2 services]... but it might be possible to do both.
Is the client's office located in either City-1 or City-2? I'm assuming that the client is currently ranking for [City-2 services] because that's what it says on the client's website. Is that the case?
PS...
They don't want to advertise in all of the City-1 Metro area but mostly just on the west side.
Also, again, we talk about organic rankings on this forum, and you're mentioning "natural listings", but then you say you
"don't want to advertise in all of such and such an area". Advertising is something else again. Natural results are achieved by modifying the actual content of the site. Advertising is achieved by changing the ad campaign. Two very different areas.