Rayden54, I know nothing about hickory.
Some trees are fairly good neighbors to an annual vegetable garden. Some are not. I am in a battle every year with the roots of Colorado spruce near one garden. A short distance away is a garden with 5 trees as neighbors, all within about 50'. None of these trees are a spruce and none cause much trouble for the veggies I grow in what I call my "Shady Corner" garden.
Here is what I think is an important question -- what time of day do your beds receive sunlight?
I find that I cannot grow much in one garden if I plant too close to bushes that shade the beds during the morning hours. Despite sunshine from mid-day on, plants do not grow well if I put them where they miss out on morning sun.
The Shady Corner garden has light at sunrise. By about 10:30, the first shade begins to fall on the garden but a good part of it will have continuous sun until 1 or 2 in the afternoon. The 5 trees are to the west and southwest. Sunlight breaks thru them for a few minutes off and on thru the afternoon on just about all of the garden. I think that helps the plants but it sure isn't much sun by mid-afternoon.
Plants grow best in the sunniest part of the Shady Corner but some do okay even where there are hours and hours of afternoon shade. It is something of a "salad garden" for me and actually does better than out in the open ground for the leafy greens during the first weeks of our hot, dry summers.
Lettuce, spinach, bok choy, and green onions grow there. I sometimes have quite a few basil plants throughout the beds. On the sunnier ground, I grow leeks and parsley. I've also had celeriac (celery root) and even some winter squash that have done okay in the sunnier spots.
It might help to think of things this way: A plant begins life as a thin root with leaves. The leaves may be useful to the gardener. It requires more light for the plant to flower, produce fruit and finally seeds. You may be able to take your plants to the flowering stage - broccoli for example - but your tomato plant may need a good deal more sunlight to produce fruit. Sweet corn is valued for its seeds but may never make it to that stage.
I hope that is of some help.