Native to North America:

Fruits:

American elderberry (Sambucus canadensis; Adoxaceae)

American grape: North American species (e.g., Vitis labrusca; Vitaceae) and American-European hybrids are grown where grape (Vitis vinifera) is not hardy and are used as rootstocks

American mayapple (Podophyllum peltatum; Berberidaceae)

American plum (Prunus americana; Rosaceae)

American persimmon (Diospyros virginiana; Ebenaceae): Traditional for desserts and as dried fruit.

Beach plum (Prunus maritima; Rosaceae)

Black cherry (Prunus serotina; Rosaceae very popular flavoring for pies, jams, and sweets.

Black raspberry (Rubus occidentalis or Rubus leucodermis; Rosaceae)

Blueberry (Vaccinium, sect. Cyanococcus; Ericaceae

Buffaloberry (Shepherdia argentea; Elaeagnaceae), which grows wild in the prairies of Canada.

Paw paw (Asimina triloba; Annonaceae)

Canada plum (Prunus nigra; Rosaceae)

Canadian serviceberry (Amelanchier canadensis; Rosaceae), also called Sugarplum

Chokecherry (Prunus virginiana; Rosaceae)

Cocoplum (Chrysobalanus icaco; Chrysobalanaceae)

Concord grape

Cranberry (Vaccinium oxycoccus; Ericaceae)

Dewberry (Rubus, sect. Flagellares, American dewberries; Rosaceae)

False-mastic (Mastichodendron foetidissimum; Sapotaceae)

Florida strangler fig (Ficus aurea; Moraceae)

Ground plum (Astragalus caryocarpus; Fabaceae), also called Ground-plum milk-vetch.

Eastern May Hawthorn (Crataegus aestivalis; Rosaceae, better known as mayhaw.

Huckleberry (Vaccinium parvifolium; Ericaceae)

Maypop (Passiflora incarnata; Passifloraceae), traditionally a summer treat.

Pawpaw (Asimina triloba; Annonaceae), not to be confused with Papaya (Carica papaya; Caricaceae), which is called pawpaw in some English dialects.

Prickly pear (Opuntia spp.,; Cactaceae) used as both a fruit and vegetable depending on part of plant.

Red mulberry (Morus rubra; Moraceae)

Pigeon plum (Coccoloba diversifolia; Polygonaceae)

Salal berry (Gaultheria shallon; Ericaceae)

Salmonberry (Rubus spectabilis; Rosaceae)

Saskatoonberry (Amelanchier alnifolia, Rosaceae

Saw palmetto (Serenoa repens; Arecaceae)

Southern crabapple (Malus angustifolia; Rosaceae)

Strawberry (Fragaria × ananassa; Rosoideae)

Thimbleberry (Rubus parviflorus; Rosaceae)

Toyon (Heteromeles arbutifolia; Rosaceae)

Wintergreen (Gaultheria procumbens; Ericaceae)

Vegetables/Grains:

Chives (Allium schoenoprasum; Amaryllidaceae)

Echinacea (Asteroideae heliantheae; Asteraceae)

American Ginseng (Panax Quinquefolius)

Araliaceae

Maple Sap (Acer; Hippocastanoideae)

Pole Beans (Phaseolus coccineus; Faboideae)

Pumpkin (Cucurbita; Cucurbitaceae)

Tomato (Solanum lycopersicum; Solaneae)

Sage (Salvia apiana; Lamiaceae)

Squash (Cucurbiteae cucurbita; Cucurbitoideae)

Sunflowers (Helianthus annuus; Asteraceae)

Jerusalem artichoke (Helianthus tuberosus; Asteraceae), also known as topinambour

Wild Rice (Zizania palustris; Poaceae)

Nuts

Acorn (Quercus alba, Quercus gambelii, Quercus kelloggii, Notholithocarpus densiflorus; Fagaceae)

Black Walnut (Juglans nigra; Juglandaceae)

White Walnut (Juglans cinerea; Juglandaceae)

Hickory nut (Carya; Juglandaceae)

Pecans (Carya illinoinensis; Juglandaceae)

Shagbark Hickory (Carya ovate; Juglandaceae)

For your New World crops, maize(corn), potatoes, tobacco, squash, beans, quinoa and chenopodium are a few species of plants that were generally used across the New World, with an expectable degree of regionality. Wild rice was also used, but not domesticated, and was used heavily in areas in which other crops were not as relied on.

I don't know how to cite this as this is kind of basic info for anyone who works on pre-Columbian sites in the Americas, but feel free to ask any other questions you may have. I love this stuff haha

In addition to the already-posted answer, the key word you might want to look up is “Columbian exchange”.