Need a good recommendation for trip with graduating senior this summer

My daughter told me the only thing she wants for a "senior trip" this summer is to go with me on a 3 day backpacking trip where we can summit a "name worthy mountain" (her words). I live in California but sometimes I get tired of the Sierras because of all the people and permitting. And they are a bit too dry at times. Options I'm thinking of are 1) Wind River Range 2) Something in Idaho, maybe in Frank Church wilderness, 3) High Uintahs in Utah.

I'd also consider something in Montana or Washington. Any suggestions on something that meets what I'm looking for?