I would consider a great deal in almost any neighborhood and I would consider a good deal in a bit better areas. With a bit more experience managing properties I feel like I can be a bit more aggressive in up-and-coming neighborhoods, but it'd have to be a killer deal to invest in some parts of the West End because I've turned down some $5-10,000 deals that cash flow like crazy. I may think differently if I was a full time investor and had the time. I would suggest getting a bit nicer of a property for your first few investments instead of something that is going to run you ragged with repairs and difficult tenets. You wouldn't want to be a landlord very long in that situation.
I'd also consider proximity of your properties. I notice that my closer properties get more attention... Maybe I'm lazy, or just don't like sitting in the car all day.
Highlands is a great area and I live there myself, but I'm not sure about cash flow. I do not have any investments there and have really not looked at the market rents, but I love it here. Per Sq Ft Sales prices seem to high to turn a profit renting them.
I also believe that a unit with 20 paid applicants before you moved out means it was probably listed below the market rate.
I'm also interested in Portland with the Portland Investment Initiative and all of that hype.