Nothing wrong with the 395/3/33 route. Google Maps suggests 3 routes, all about the same distance and time.
donn0128 mentioned 20, but also visiting Dry Falls and the dam. 20 isn't close to either of those. US2 is close to those, but seeing both of those adds 60 miles to your drive. I like those sights, but the drive from Spokane to dam is lots of flat wheat fields.
W20 from Kettle Falls to US97 is ok, but crosses the highest paved pass in Washington. It's not hard, but that part of 20 is not as scenic as the part over the Cascades.
Stops and sights on the 395 route:
- camping Roosevelt Lake around Kettle Falls
- camping a Christina Lake
- historic mining district at Greenwood
- camping at Kettle Valley
As for the gas issue - you are going to enter Canada sooner or later. There is only a 70 mile difference in the length of the Canadian portion among these routes. There's nothing special about gas prices in small towns of NE Washington.
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Another thought - US97 in northern Washington follows a major a valley with light traffic. There is a nice state park just before the border. 97 in BC is a lot busier, with lots of orchards, vineyards and vacation homes. It's the warm playground for BC. It is 4 lanes from the junction of 97c north. 33 bypasses a portion of this heavier traffic.
97c is an alternative to 97 from Kelowna to Cache Creek. It climbs on to a plateau around Meritt. If I were coming north on 97 I'd take 97c to bypass Kelowna, Vernon and Kamloops. If using 33 I'd probably stick with 97.
