what grows well with grape vine?

Grapes are very deep-rooted, and hold their own quite well with a shallow-rooted groundcover beneath them, even one that forms a mat, like mint. Dutch Clover, or, as someone suggested, daylilies. Generally speaking, root competittion, and competition for space are not the big considerations for grapes that they would be for less vigorous crops.

HOWEVER, everyone has their vulnerability. With grapes, it is the specter of virus infection from sucking insects like aphids and leafhoppers. This is a serious problem, even leading to the abandonment of vineyards in affected areas. So resistance to aphids and leafhoppers, as well as other sap-sucking pest, is the prime qualification for a grape understory plant.

So for example, phacelia--which is a stellar cover crop and pollinator plant--would be off the table because it attracts sap-sucking lygus bugs. Make use of the county ag department or cooperative extension service to find out what is common in your area. You don't need to follow their suggestions about pest control, just find out what pests are around and causing problems.

I have seen research that the essential oils and terpenes in Chamomile repel aphids. That might be a start. Many herbs and perennials seem to be untroubled by pests. They might be good choices.

Roses are traditional here as a canary crop (show bug or illness first before the grapes show symptoms).

I usually only have one vine and somehow it always ends up surrounded by rhubarb.  Don't know if they help each other or if it's just because they are both perennial, they get lumped together.

It depends on your permaculture plan.  The vines will provide a lot of leaves for shade in summer and mulch in winter.  depending on east/west or north/south orientation you will have a sunny side and a shady side or morning and afternoon shade.  Grapes seem to have a strategy of putting down deep roots for water and feeding the soil with sugar water with their surface roots So yes rhubarb with its large leaves shades the soil so they work well together.
I just mowed the grass between three rows in N/S orientation and it was twice as tall as the rest of the lawn.   The rhubarb is more than 50 years old and makes stalks 1 inch thick and 16 inches long.