If you would like, I would be happy to meet you and give you the tour of the Eugene area, its neighborhoods, where interesting things are, where the school districts are (but as noted below, cannot recommend schools), good restaurants, etc. I had a realtor do this for my wife and me when we moved here 7 years ago, and it was a great gift. I would be happy to pay it forward.
Good luck! Dohn Riley
Hybrid Real Estate
If no property managers respond, which don't expect, I suggest that you Google Eugene rentals or something like that and you will have plenty of hits to work on.
Again, welcome and enjoy,
DiMar Real Estate