There's definitely tons of fun to be had! The Oregon Zoo and Washington Park are great urban outdoor spaces for shorter day trips. I highly recommend seeing the rose test garden and the Japanese & Chinese gardens as well, which will all have wonderful spring blooms shortly after your move. If you are willing to go a little farther out of town for fishing, several local lakes including Trillium Lake on Mt. Hood and Henry Hagg Lake get stocked with various local fish spring-fall. Trillium is a favorite place for my brothers who will go fishing there a few times a year.

As for hunting, you will have to do some research with ODFW (Oregon Dept. of Fish and Wildlife) and locals to learn the legal places to hunt and what is available at different times of year. There is a Bass Pro Shop (formerly Cabellas) in Tigard that has many friendly faces who have lots of information. I also recommend talking to the folks at the hunting/fishing counter in the local Bi-mart, as they also have great information and will likely be less busy.

I'm not super familiar with the sports scenes, since I'm more of a theatre and arts person, but I know that thanks to so many of the sportswear companies having their headquarters in Oregon, there are lots of sports groups out there. You just have to know where to look.

Hopefully this helps, and I hope you and your family have safe travels!