There are pretty limited riding opportunities for rides of that length around here. If you want to ride flat terrain amongst the grass farms, you can go north of town. Bear in mind that some of the commuters from the suburbs are none too tolerant of bikes on "their" roads, so plan your times accordingly (or just deal with the hostility; it's not generally violent). As the day wears on, the wind generally picks up from the north, so the ride home is always faster than the ride out. A slightly less flat option exists as a loop just south of town by going over Fox Hollow. I like to go up from West Amazon, drop down to Lorane Hwy and then return back up McBeth (weird spellings around here) to the top of Fox Hollow. Longer loops that include Briggs Hill Rd and Doane Rd involve riding on Territorial Hwy, which can be just fine if you pick your timing but is unpleasant when the commuters are rolling.
If you're willing to go a bit further afield, we have some absolutely awesome riding opportunities that start about ten miles west of town. If you stay here, Velo Bed and Breakfast
, then you are eight miles from Wolf Creek Rd. Twelve miles and two climbs later, you're in the O&C (Oregon and California Railroad lands), which are tree farms run by BLM interspersed with private tree farms along the Siuslaw and Smith Rivers. There are a couple of nice century-length loops from the Velo B&B that are almost too nice to describe. Ride fifty miles, take a long break eating a picnic along a river, and then ride another fifty back. There are a couple of pioneer cemeteries to hunt down out there if you're into that sort of thing. No services in the O&C (no cell coverage either), so bring what you need. If you are feeling adventurous, you can ride eighty-five miles to the coast along the Smith River, stay the night in Reedsport, and then ride home.
Eugene is small enough that it doesn't matter much where you stay in terms of your rides. However, various neighborhoods have their own characteristics. If you stay anywhere near the university or the west side of town, everything needs to be locked down; we have a lot of petty theft here. Similar problems downtown and in the Whiteaker. If you rent something on the south side of town, you should have better piece of mind for your possessions, but take a good look at the roads you'll be on going to and from the activities you will be partaking of. Not all roads in town lend themselves to joyful night rides home (we have a huge drunk problem here, particularly amongst the suburban population, so you don't want to be on a road they will be taking home in the evening).
I know that all sounds so dark, but I don't want you to naively think you can lock up a nice bike with a cable and then lose it to some thief. We don't have much if any violent crime (walk the streets with confidence; even our homeless folks are friendly). The people are almost universally nice and helpful and, if you like brew pubs we have several that people seem to enjoy. Most venues are big on live music, so if that's something you like you should be able to find it with ease. My favorite feature is the large number of small grocery stores with high quality food, but then I'm a glutton.
Have a nice visit. If you want specific routes, let me know and I'll do some ridewithgps routes for you.