It's only a matter of time before the decomposed granite makes its way into the grass.

I wouldn't want any loose material around the hot tub; even with pavers between you'll end up with grit in your hot tub. If you do go that route, you'll want to use a real edging material...either concrete edging, plastic, small boulders, or steel to create a nice finished edge. A trench of river rock will not keep the granite from mixing in, and keeping the grass edged along the river rock will be time consuming since grass can creep into the rock area. I would suggest using pavers and polymeric sand between the joints around your hot tub area.

I've got areas of complete gravel in my yard and no grass has tried to take root there in the 6+ years we've lived here. These areas don't butt up to grassy spots though, but rather to mulched flower beds. Perhaps a buffer of beds, combined with solid edging (steel or plastic edges) would keep weeds and grass at bay.

You are lucky Kathryn, I have some at the side of the house, not near any grass, after spraying, which I hate to do, weeds start back in a month or so.