Duke's right: With sometimes heavy concentration of salmon fishermen on the Clearwater, the Snake would be the better place to take your boat for an inaugural spin.
As for what section of river, that depends on what kind of water you want to experience. If you're just looking to do a few turns, you can use one of the many ramps in Lewiston (or Clarkston). Slackwater on the Snake stretches from the much-maligned Lower Granite Dam to Asotin, which is about eight south of Lewiston-Clarkston. If you're looking to do some actual river running, you can trailer down into the beginnings of Hells Canyon -- to Couse Creek, about 10 miles south of Asotin, or Heller Bar, some 15 miles farther. The Snake is at typical spring-runoff levels, consistently above 50,000 cfs, so you don't have to concern yourself so much with channels and/or obstacles.
So what'd you lay out for? A Custom Weld? Thunder Jet? Duckworth? It's amazing that a community this size contains so many boat manufacturers, and quality ones at that.