I'm in a helpful mood, so here's all I know about the running stuff:
They do, in fact, let just anyone on the Hayward Field track. They recently installed a Lanes 1-4 blockade (grrrr), but I haven't yet seen it in blocking position, so it might be open for you. The closest other 400m rubberized track is at South Eugene High School; the track is on the corner of 24th Ave and Amazon Parkway. (You can find it on Google Maps pretty easily.)
Across 24th from that track is the Amazon trail, which is bark and has loops of 1000m, 1600m, and 1 Mile.
Further South from Amazon is the Rexius Trail, which is barkdust (so soft) and is on both sides of Amazon Drive between 33rd Ave. and Martin St.
My favorite trail is the Ridgeline Trail, which is six miles long and goes from Blanton Road to Spring Street, and crosses Willamette, Fox Hollow, and Dillard Road. It can also be accessed via a few streets/trails near the top (South) end of Rexius.
The other good trail network is Pre's Trail. From the U of O campus, go North on Agate, and cross the Autzen Footbridge, and there'll be a bunch of bark trails you can go on there...if you continue on the main path towards Autzen, there's a map of the main sections of Pre's Trail.
That should be enough places to fill up your weekend, even if you're running doubles.