Most maps color National Forests, and in the West those are mostly mountains. Print maps also show the height of passes. Pass heights are also available on the state DOT websites, especially if they track winter pass conditions. In WA passes range from around 3000ft (I90) to 5000 ft (WA 20, Sherman).
Google Maps in Terrain mode shows mountains and valleys, and at certain zoom levels shows altitude contours.
GPS units show altitude as well as position. If you have a smart phone, even without data plan, you have GPS.
Washington is all below 5000 ft except for a few passes.
In Oregon, Lakeview bills itself as the highest town at 4800, Bend is 4000. OR138 on the north side of Crater Lake is, I believe the highest pass at 5600. Crater Lake rim is 7000.
In California, the Sierras passes get above 5000. Reno is 4500 (Wiki), Lake Tahoe 6200. Much of the NE corner of CA is above 4000.
In Idaho, the mountains get above 7000 (Stanley), but Lewiston on the Snake is lowest, with surrounding plateaus around 2-3000. Boise and most I84 is just a bit higher.
Denver is known as the Mile high city; that's on the wester edge of the Great Plains. Grand Junction on the west side is 4500.
I80 across WY spends a lot of time in Great Basin, the continental divide in that area. So a lot of that is at the 4000+ altitude.
Yellowstone Lake is about 7000.
I40 from Flagstaff to Gallup is relatively high; again crossing a broad divide.
On a cross country trip, to minimize time above 4000, I'd cross Montana or southern Arisona/New Mexico. In between you'd spend at least half a day above that.
