If you want to fish trout in the Spokane area I would recomend going to the lakes in the area between Cheney and Sprague. My best experience has been Fishtrap, and early in the season Fish lake, which is closer to Spokane. Fishtrap will have bigger fish, but there should be an excellent chance of catching plenty of trout in Fish lake in early may. Don't go there in july though. There's also sunfish in Fish lake, whereas Fishtrap has some catfish.
Fish lake is closer, about 20 min from Spokane, probably about 45 min from Liberty Lake. Fishtrap is about 45 min from Spokane, which would be a little over an hour from Liberty Lake.
Both have excellent fishing access for kids. You'll have to pay $ 3 pr. person (not sure what the age limit is for the kids to fish free) at the Fishtrap resort. At Fish lake you might have to pay a couple of bucks too as it is now a park, but I don't think they start charging until late june when the lifeguards is on duty.
You can try Liberty Lake first. I havn't fished there for a couple of years as I do not care for the way they buildt the dock there (I don't have a boat), but I did catch a trout there once. My brother in law caught a bunch of catfish there 2 years ago, and claims it holds quite a bit of bass, but I've never seen any.
I've tried Newman Lake from the boat launch several times, but never caught anything, nor have I ever seen anyone catch anything. There's supposed to be record size tiger muskies in there, but you probably need a boat to get there or go to one of the resorts. I don't know how much they charge. Be aware that the WDFW is doing some research until some time in may or june and the tiger fishing is limited.
Jes