I live on the coast now, so I'm not against giving any secrets away! However, depending upon what you want to fish for,there is excellent fishing in a lot of lakes in the area that you can drive to and launch a float tube. I really wouldn't get hung up on the idea of having to do the hike-in thing if all you're looking for is good fishing without water skiers.
One of my favorite lakes is Sprague, just a few miles from Cheney. There are tons of walleyes, trout, bass, and big bluegill. The lake tends to green up quickly, which can be a negative for a tuber, but the fishing can be spectacular. I would also look real close at some of the smaller trout lakes: Amber and Williams come to mind. Then there's my favorite: Silver, but it tends to get more boat traffic. Medical is good as West Medical used to be. You can also drive a bit and do the float tube thing at walk-ins below the Potholes Reservoir, but that is a bit of a drive. The fishing can be very good. Just check in at the Mardon store for the latest info. If you buy something, they're pretty good about giving you the straight scoop.
If you're thinking about spring, check the regs and hit the winter lakes just after the ice leaves. You need to wear all the clothes you own if you're in a float tube, but the trout fishing can be really good for fat fish.
I can't make more specific recommendations beyond that because I haven't lived there in four years, but I can say that there is some very good fishing in the lakes around Cheney. West siders don't know the half of some of the lakes... such as Roosevelt or Banks. Both have fantastic trout fishing in the winter/spring, and the trout are BIG, really big. Moses and Potholes both have big trout as well, and I wouldn't be afraid to tube in either before the skiers get out.
I would be careful about safety when tackling the larger lakes, however.