There are lots of apartments here, being a college town, and many of which I am sure would fit your needs for that price or even less. We are renting a 2 bedroom in a very nice area of Eugene where the schools are excellent, crime is almost non-existent, and we're right on the bike trail and walking distance to everything we need (market, bank, post office, etc.). We are paying around $700/month for 1050 sq. ft. plus storage space. We also have a sweet little yard to garden in and we rent a garage as well. We love it... aside from the fact that there's no swimming pool and no air conditioning.

It's saving us a bunch of money while we look for our first home to buy. We are a family and our kids are comfortable here, too.
We have moved around lots for my husbands job... from state to state... and I found this place by looking around on the apartmentratings.com website. You might want to check that website out if you haven't found it already. Don't put too much stock into all the negative reviews posted there, though, as many renters seem to use the place to vent unwarranted issues. I always sort of "read between the lines" when I'm browsing there. We are in the 97408 zip code. It's a good, safe, and fun area - especially with kids.
Good luck with everything!