I was in Eugene with my bicycle in 2005 (got pics in this set:
http://www.flickr.com/photos/1430288...7602332365295/).
I had to stay there overnight because of Amtrak, and decided to ride a while in the morning before catching the Greyhound out of town. The guy at the motel wasn't at all sure about me riding around Eugene by myself and warned me several times not to let my bicycle out of my sight. Then when he heard I was taking my boxed bicycle and all my gear down to the Greyhound station in a taxi, he just about lost it. He gave me very detailed instructions about being sure to check in all my luggage and not wandering too far away from the station while I waited, etc.
The area where I cycled wasn't bad, but the area around the Greyhound station was a bit scary.