The Nevada side of Lake Tahoe might suit your needs.
I can't speak to the guns thing, here in NV, but I think we're relatively liberal (i.e. libertarian) on gun laws here.
Lake Tahoe property values are pretty well insane. But if you could afford to live in, say, Incline Village NV, I think it checks most of your boxes other than being low cost of living.
Problem I see with your needs are great schools, mountains, and low cost of living. I think you get to pick two of those three. mountain communities with good schools are going to be expensive. More remote mountain communities/small towns are going to be affordable but schools not so good.
I guess we also need to understand what your expectations are when you say "living in the mountains"? Nevada has lots and lots and lots of mountains, but many of them are pretty barren and arid. Take a look at the Virginia City Highlands area outside of Reno, near Virginia City, NV for example.
My go-to answer would've been Douglas County, NV (Minden/Gardnerville) 20 years ago, but these days I think the secret is out a bit. Still a great place to be ... an hour south of Reno, semi-rural, temperate, and close to both Tahoe and the eastern Sierra (Mammoth, Yosemite, Mono Lake, etc etc) without living in CA.
California expats move to Northern Nevada every day.