I think that Gonzaga and Oregon State are both great suggestions. Run the Net Price Calculator (NPC) at Gonzaga though, as it may not hit budget. The schools below are all ABET-accredited for most of the main engineering disciplines and might be worth checking out.
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Cal State: Chico is one of the few residential Cal States, has several engineering and engineering technology majors, about 13k undergrads, and is part of WUE which means a discount for Washington residents.
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UC-Merced: The only UC that’s part of WUE. It’s the newest UC campus which means that many California residents find it less than desirable, but it’s already #60 on U.S. News & World Report’s ranking (which only means as much as you want it to mean…but I’m using it here to show that this campus is no slouch). Since it’s not a super-popular UC (yet), that means that there’s a lot of flexibility in terms of choosing and switching between majors.
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U. of the Pacific (CA): About 3300 undergrads at this school that’s ABET-accredited for several different engineering disciplines.
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Portland State (OR): About 17k undergrads. This school has more of a commuter population, but 36% of first year students live on-campus, so there is a certain cohort within a residential community here.
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Seattle U (WA): About 4k undergrads
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Seattle Pacific (WA): About 2400 undergrads
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U. of Portland (OR): About 3400 undergrads
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Santa Clara & Loyola Marymount are mid-sized possibilities, but I’m less confident of them coming in as affordable.