My husband and I have been together going on 15 years and we are raising two kids together - one who is in elementary school and one who is in middle school. We currently live in Eugene.
We have bounced around from state to state, and city to city, quite a bit for my husbands job. This is actually our second time living in Eugene! We lived here for three years, LOVED it, but then relocated for what my husband at the time thought were greener pastures (Seattle area). We were so unhappy after having realizing what we had given up (our happy life in Eugene) that we came back as quick as we could, and are planning to stay at least until the kids finish school.
If you are an outdoorsy, laid-back, tolerant, simple and quiet kind of person who appreciates art, music, books, nature, etc... I think you would really love the opportunity to raise your children here. Just keep in mind that Eugene is NOT California. It's not the east-coast, either. It's not about appearances here - how you dress, the car you drive, your hairstyle, etc. People dance to the beat of their own drummer here. There's a very strong "live and let live" mentality. People for the most part also tend to keep to themselves. You'll probably make friends with people you work or volunteer with... but we've found that in general Pacific Northwesterners are not a gregarious bunch. The old-timers/natives kind of already have their group of people and they are a close-knit group... and for outsiders we kind of slowly find our friends... but it's a very different sort of place socially than anyplace my husband and I have ever lived before. Maybe it's the weather? We personally like it, as we are boring homebodies who don't party or drink or go to bars or anything like that... but I can see how for younger people, or people who do like to go out, how Eugene might not be a good fit for them.
As far as whether or not Eugene has good schools, I feel that's a hard question to answer. People have different ideas on what makes a "good school". You can take the national test scores and throw them down the garbage... with the changing curriculum all across the nation and the fact that most state standardized tests do not change along with the curriculum... the tests do not truly show how the schools are performing. It's kind of a joke, to be honest. Not to mention the fact that many schools who do score very highly on those tests do so because they neglect other areas to drill the kids on the test material for that specific purpose. Years ago I used to place a certain amount of trust in those kinds of things but now I view them as a waste of time. You're better off visiting, talking to teachers, talking to parents, and just going in and getting a feel for a particular school. Also even within one district there will be some schools that will surprise you while others disappoint.
We have experienced several different school districts in several different states and for our kids and our family priorities Eugene fits us best. But it's a very personal thing. We feel the arts are important as well as strong academics and a focus on the humanities and environmental sciences. Eugene has this, and also stresses the importance of allowing children time to be children - time for family togetherness and play. We've lived in other places where the schools were supposedly rated the "highest in the nation" but we weren't happy with the schools at all in those places. Too competitive, too stressful, too much homework, too little time left for family time or relaxed playtime. So as far as whether you'll like the schools here, it just depends on what your idea of a good school is.
Jobs are an issue here... that's for sure. I wouldn't relocate here without a job lined up first. It's one of those places where you're better off knowing someone who knows someone else who can refer you and get you a position with someone they know who has an opening. If that makes sense?

And $350K will buy you a very nice home in a good, safe area.