Maybe you could "fence" them with a border of marigolds and or perennial alliums and or daffadils. Things the critters in my parts haven't eaten are: broccoli, squash plants (when bigger, both summer and winter), tomatoes, cape gooseberries, radishes. I think that all of these things are still tasty morsels when they are young seedlings.

No deer? Anyway, only potatoes will work well there. Fortunately, it is a large crop. I know we could eat 200lbs a year. My groundhogs do prefer various brassica, and rabbits prefer chicory, but it is only because there is a choice. Potato plants are toxic and I have always grown them outside the fence with success, even with very high deer density.

I would consider trying small patches of eggplants and peppers. These plants are not bothered much by varmints. Of exotic vegetables, I would try sunchokes, parsnips, cardoon and florence fennel. Mine have never been bothered by rabbits or 'hogs. None of these options would survive deer, though.

I have the same situation (deer especially). Garlic and onions can be planted in the open areas and are left alone. Herbs are another thing often left alone.

parsley, pots, rocket, squashes. mint, cilantro, carrots, red russ kale.

No way kale or squash survive a groundhog assault. Irritatingly, groundhogs will take a bit out of each squash, ruining them all. And groundhogs will eat onions with gusto.
Deer will eat everything of course.

That is a really tough crowd to discourage. Peppers, garlic and lavender would all work.

I have given up on hoping the fence will keep them out of my garden. Cute little quail fly in and tear up my new sprouted seedlings. Sometimes I will cover new plants with a self made cage of wire, but the big dog helps the most.

Not sure about chipmunks, but the other animals mentioned probably would not touch okra.

Thanks to all. I think I'll go with potatoes (I did some a few years ago) and test out the border flower recommendations for effectiveness around a couple of test beds of more susceptible vegetables.

Tuckers, I've gardened in four states, just in the USA. Deer seem to behave differently, in different locations. For instance, take potatoes: in some places they don't bother them. In others, they do. Anywhere I've been they devour okra. When we lived in NJ I had squirrels raid the garden and run up trees with tomatoes in their mouths.

Like I said, deer behave differently in different locations and circumstances. In NJ I doubt I could get away with it. There the deer were so populated that they ate things they normally would not. But here in OK I'm pretty sure I could grow a non sweet corn, potatoes or most aromatic herbs. Also, here, I've successfully grown winter squash out in the open. Neither the deer nor my goats (insert exclamation points!!!) tend to bother the squash. But groundhogs/woodchucks, now they're really bad! Unless one can eliminate them that would probably knock out the corn and squash.

George
Tahlequah, OK