The most convenient way is on iNat at home on your phone or laptop. Filter by your area and use the map-view. This will probably show you escapees that might have sprouted from adjacent human activity.
Depending on your climate, it may not normally grow in your area, so the next best thing is to walk the taxonomy-tree, to see if any relatives grow in your area: look at your target, Solanum tuberosum and click the Taxonomy tab. You can then filter your area for Solanum, many of which are poisonous, but also includes tomato. At the least, it gives you an idea of where related species grow in your area and what types of areas they prefer (canyons, ridges, floodplains, etc.).
This is also a nice way to find wild relatives in your area. For example, in my area, there’s early onion, which looks a lot like a regular yellow onion, but the bulb is the size of a fingernail!
Also, based on some observations I’ve seen or identified, hiking & biking trails are another source of wild vegetables, for example: tomato, pumpkin, and sunflower. The only really wild vegetable I’ve seen is this wild celery, possibly.
I read “genuinely wild” differently. I took it to mean the original, ancestral population from which the cultivated forms were domesticated. Or at the very least, sprouted from “true seed” dispersed by wild vectors. I don’t count waifs as truly wild.
The early onion looks cool, and it seems they are indeed native to California!
As @jasonhernandez74 guessed, I was thinking about the original population of potatoes, in a habitat reached by wild vectors. (Or similar species, as long as they’re wild. I have now checked: Fendler’s Horsenettle has a native range extending to the US.)
My hope, alluded to in the post, is to film a wild animal digging up a wild potato tuber and eating it as part of it normal diet. In other words, I want to see for myself the role of potato tubers outside of human activity.
I can’t find any footage of that on the internet, so I don’t know if it’s a realistic aim.
It might be easier to locate the wild ancestor of the tomato, the currant tomato which is in Ecuador and Peru, and frugivorous birds that would eat it.
It depends how you are defining “potato”. What we usually think of as potatoes (i.e., the domesticated edible tuber) doesn’t really exist as such in the wild.