Hi Elizabrooke:
We live in an area in the Southwest part of Beaverton, close to Murrayhill. My recommendation will be to identify the schools you are interested in, and then look at the neighborhoods. If you intend buying, rmls dot com is the listing of the houses for sale in and around Portland, and you can search for houses by the specific school you are interested in.
When we were looking to buy, we looked at Lake Oswego, West Linn, SW Portland and Beaverton. Unfortunately even then we could not find the kind of house we wanted for the kind of money we had, in Lake Oswego, West Linn and SW Portland. Beaverton worked for us... and we have been happy here.. though we too are looking to move.. to the East coast

As for areas to avoid. Generally if you go by the school ratings... the highly rated schools tend to be in decent areas.
Good luck with the search over the weekend.. there are a number of houses in the market where we live and a good amount of new construction going on, so come on by.
Pdxer07