I ended up purchasing this outdoor kitchen island thing off Amazon.
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Pro: it's waterproof and keeps anything inside it dry
Con: there are no internal shelves so everything is piled up inside
It is convenient for having all the usual stuff I need close to the grills (tongs, spatulas, fire-starters, etc.) but it's far from a complete solution.
I suppose that shelves could be added -- Good suggestion. They'd have to be free-standing inside it (like little end-tables or nightstands) because there's nothing inside to anchor shelves to.
Actually, my bigger concern is my charcoal (it's guaranteed to rain if I forget to bring them back to the porch!).
I also have one of those outdoor island thingies. I made a free-standing shelf for one side of the cabinet, kinda like an old monitor stand (remember those). Charcoal fits in the other side.
I've had it for 2 or 3 years now. It's partially under my porch roof but still gets wet when it rains. So far so good. The top is stainless steel, but it can discolor some and show brush marks from wiping it down.