For weighing a personal vehicle that is not at risk of being over weight, I like the ports of entry south of Pocatello. They have a digital readout to tell you the weight of each axle or group as you drive over. Best bet is late at night when they tend to be closed (otherwise, you may have to abort if there are lots of trucks).
Public scales include Wright Bros truck stop on US-20 at Holmes, about a mile east of I-15 exit 119; and Forde Johnson about a mile toward Pocatello from I-15 exit 67. Last time I used each of them, they charged $6 to weigh. Wright Bros has multi-pad scale that gives axle readings and gross. I recall Forde Johnson is a single pad, so you have to pull on gradually and get them to take readings for axle groups.
Doug Andrus distributing on W. Broadway may still have a public scale, too, but it's been about 15 years since I tried there. They did not charge me to weigh a personal vehicle.
Happy scaling!