Where might one stay in a residential rental to enjoy the coffee shops and street life of the gentrified Portland neighborhoods.
Recommended
Portland Neighborhoods
45.5289870, -122.6817298 Perl District more 
45.5269140, -122.6985312 Northwest Portland more
45.5508259, -122.6755285 Mississippi Aveneue more
45.5507890, -122.6667041 North Williams more
45.5590522, -122.6419365 Alberta Arts more
45.5047935, -122.6335037 Division more
45.5120416, -122.6258379 Hawthorn more
BOUNDARY
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Travel Portland appears to be a good overview of the major Portland neighborhoods. Any of them other than Old Town and the Central Eastside should meet your criteria. Actual, most of the Google search results for “Portland Neighborhoods” look pretty useful including maps, etc.
See Street Map or Topo Map
See Biketown for nearby city bike rentals.
These are some less hip places around Portland that have well known geo coordinates. I add them to show how map markers move between pages. Shift-click a link to pile them up in the lineup.
Portland Confluences that I've visited.
2001 Geocaches that I've placed.
Ward's Home Page where I've lived all my life.
Looking for bike share in Eugene? See Peace Health Rides or try the pub tour of McMenamins of Eugene