Notch and Nonotchka are used to us now, and usually come scampering right up when we show up with food. But sometimes they're leery and decide it's better to sneak up on the nuts so they don't run away.
They like walnuts best, but they're perfectly happy eating hazelnuts or pecans. They don't like chestnuts much (at least raw, haven't tried toasting one first) and they don't like peanuts (which is just as well since a number of sources say raw peanuts are bad for squirrels). They like "tart Montmorency cherries" from Trader Joe's, but they don't like raisins or the cheaper "Rainier" cherries, or barberries. (Which matches my own taste almost exactly, except that I like barberries mixed with other things.) They don't like fresh fruit, like apple cores (though we've since had other squirrels who liked them).
Nonotchka can eat seven or eight walnuts one after the other before she starts to lose interest. I don't know where she puts it all.
They have zero interest in birdseed, dried wheat or corn.
They love red oak buds, when the tree starts sprouting, and occasionally nibble other vegetation in the garden, like a chard leaf or a bud from the trumpet vine.