Eugene police call log (beta) | The Register-Guard
Research the Police call log.
I would recommend the Far West Neighborhood around Chambers and West 18th as it is in town close to amenities, reasonable, relatively safe, away from the campus party scene, 3 miles from campus and on the bus route.
I can recommend Chinook Property Mgt,
Property management by Chinook, Eugene, Oregon
as they keep their properties in reasonable shape.
From the police log it seems most crime occurs near the campus, downtown area and the whiteacre neighborhood. Just my observations from the log.
Good Luck.