First off, congrats on finding a paying job in Eugene.
Agree with the folks above. I did most of my Eugene riding b/w 1988-1993, and agree with the folks above. Will share some thoughts below...not sure if some of these have been outlawed in the last 20yrs...if so, bummer.
Hardesty and Eula start at the same place, and have the same vertical drop. But while Hardesty does it over 6miles, Eula is only 4miles. Translation: Eula is a STEEP drop. It's a great ride, but you will be on the brakes the entire time. Hardesty will give you fabulous Jedi singletrack flow and more opportunity to open up the speed...as you can tell from the sweet videos here by erosive.
You really can't go wrong with most of the trails around Oakridge. Past Oakridge is Moon Point, boasting a big view from the peak, and a primo 8mile singletrack downhill.
Crawfish Trail, east of Cottage Grove is worth a day trip. Not much more drivetime than going to Oakridge. Campground near the trailhead. Post ride there is some cool waterfall cliff jumping nearby on Brice Creek. There used to also be a 40foot-drop ropeswing by the inlet to to Dorena Reservoir.
Hwy 126 East of Eugene/Springfield has a lot of nice rides. I'm not such a big fan of McKenzie River trail, but we used to have good times on Ollallie Trail/Horsepasture Mountain, and I recall another trail called Mt. Fuji.
Not to wax nostalgic, but when I first moved to Eugene, Spencer's Butte was open and legal to Mtn Bikes. THAT was the best quick local ride ever. We would go up Fox Hollow, ride up to the peak. The quick downhill option was to return 2/3 the way we came, but take the fork left to Willamette Drive, and bomb the steep road back to town. The longer ride was to return back to Fox Hollow, cross the road, and follow the singletrack/powerlines all the way to Lane Community College. Required a big climb-out up over 28th or 29th Street back into Eugene.
Folks used to ride on Mt Pisgah nearby too, but I never really liked the overexposed terrain and endless poison oak. May no longer be legal either.
For extremely close-to-home riding, nothing epic, there used to be 2-3 decent short-run singletracks on the southern end of Hendricks Park, and an impossibly steep face we called "The Widowmaker" that used to spit us out on the back side of Hendricks Park, requiring a loop-back to Franklin Blvd to get home. I'm guessing these have also been banned.