I think we're going to St Johns, an urbanish but way less dense than I'm usually okay with neighborhood of Portland. If we do, it will be through Home Forward (aka HAP/housing authority of portland), but even as a normal renter I was looking at going to either that area or south of Powell or Holgate soon because rents have skyrocketed since we moved here. If we go to St Johns we can easily access a huge woodsy park in addition to the rivers and lots of small parks, and there's some decent music and food nearby. Public transit and grocery store access there is not good.
I live in the 50s part of the NE quadrant of my city right now (where the river is zero/center and anything in either direction proceeds to higher numbers). We can walk downtown in about an hour, and we have access to lots of buses and grocery stores, but we're far enough out that there aren't sidewalks everywhere, and being close to the freeway means that many drivers are speeding and not expecting pedestrians. I don't plan to ever not be at least an occasional pedestrian.