HI. I have lived in Eugene for 10 yrs and have school aged kids, so I can probably answer some of your questions....
My girls go to the Family School, which is an alternative school. There are many options for schools in Eugene, but 5 elementary schools will be closed this coming year. Our district has a $27 million deficit for next year, forcing the school closings and lots of furlow days. They are trying to pass a local tax measure to support the schools, which will be voted on in May.
Although that sounds bad, our schools are pretty good to begin with. The crowding the closing of those schools will cause next year will actually just put us at the class sizes that are typically found in Portland or most larger cities. Many schools in town (such as Family School) have an extremely high level of family involvement which helps to balance the shortcomings our budget situation can produce.
The school district has "school choice," so you can enroll your child in any school in the district via a lottery which happens this month (I think). Most of the schools want you to attend one of their tours in order to apply for the lottery. But since your DD is in 3rd grade it would be easier to get her into one of these school after the lottery than if she were in Kindergarten (if they have space available, a lot of the charter/ alternative schools have caps on enrollment, but there's less competition for spots in the upper grades).
The library system is very nice. We have a beautiful new 4 or 5 floor library downtown, and I think there are a couple smaller branches too. They have great programs for younger kids such as summer reading and events for families on weekends.
Eugene is often voted one of the most bike friendly places around. We have an extensive bus system that can get you pretty much anywhere you need to go in Eugene/ Springfield. It's called LTD. We also have TONS of bike paths, lane, etc.. There is a large community of bikers here and people are very into it. I live on the out skirts of town now, but I used to live downtown and used my bike to get everywhere and it was great! I could actually still use my bike from here, the bike path is close to my house, but it just doesn't work for us b/c it's a long ride to get anywhere being so far out. Eugene is a great place for bikers. (try googling Eugene bike paths and you should be able to pull up a map).
There are several community centers/ recreation centers that are part of the parks dept which offer a variety of classes and programs for kids and adults. We also have an excellent YMCA. The parks offer free movies in the summer, some have summer camps, they do day trips for hiking/ snowshoeing, kayak lessons, swim lessons, art classes.... it's a really great resource. (Amazon Park Recreation Center and River Rd. recreation center are two you could look up).
There are lots of OG farms in the area, so we have several farms markets and many of the farms offer CSAs. The big Lane County Farmer's Market is on saturdays and shares space with the Saturday Market (the country's oldest running outdoor artist market... or something like that). We have a big, but locally owned, grocery store that focuses on natural and local but still offers some conventional products, which has 4 locations in town. And we also have 5ish smaller local health food stores. If you like food and are into organics Eugene is really great!
Overall Eugene is a really nice place to raise a family. I would like to move because I have been here so long, but I can't think of a better place to raise my kids so I stay. The town is clean, the people are friendly, our neighborhood is very safe, we LOVE LOVE LOVE our school... I could go on and on.
If you have any more questions I would be happy to answer them the best I can for you.