Many of the US rental aircraft are not covered for grass or dirt strips as these
are rarer here. Maybe you can get some extra insurance to cover that, but just be aware of it.
As a sidenote, the small grass fields I regularly plop down into in England, like Maypole and Damyns Hall for instance, are considered "bush" flying here and very seriously broached and treated by the powers-at-be. They're used to 8000ft tarmac in even the smallest of villages.
As I can only speak for California, I do think that it's a breathtaking state. You should def explore it. The Sierra Nevadas, Yosemite, Sequoia, Big Sur, Napa, Tahoe - all places that leave you speechless in beauty. I would recommend a landing at Shelter Cove airport on the coast:
AirNav: 0Q5 - Shelter Cove Airport