Before the exchange tomatoes, beans, tobacco, potatoes didn't exist in Europe....

Pretty much, although it is somewhat less true about beans. The vernacular term "Bean" refers in part to some plants of the family Leguminosae from the Americas, while it also includes others are from the old world. In the Americas, it comprises various species belonging for the most part to the genus Phaseolus (common beans, runner beans, Lima beans, etc). In the old world, it comprises a disparate assemblage of types such as Faba beans (Vicia faba), Glycine max (aka "Soy Beans") and various species of the genus Vigna such as Mung, Adzuki, Moth beans, Urad and cowpeas. The latter group (faba, soy and Vigna's) have been used in Europe and/or Asia for millenia, way before the Columbian exchange. It is only the Phaseolus types which were introduced into Europe by the Exchange.

Before the exchange cows, pigs, horses, grains, coffee didn't exist in the Americas.

Here again, pretty much, inasmuch that you take into account the presence of Maize and Quinoa in South America and of so-called "wild rice" (Zizania sp.) in North America, which by any account should all be considered grains. Note that the latter is more closely related to oats than rice, really...