I spent a year in China teaching English with a bunch of coworkers from various countries in the Anglosphere. One of the things many of them experienced was a strong craving for western foods that weren't easy to acquire in our city. As open minded as we tried to be, having little familiar food took its toll and many of us lost our appetites and a great deal of weight over time.
I'm just curious why you don't really see this aspect of foreign travel emphasized in adventure stories. Was it because food was relatively simple then, so there wasn't much difference between cultures? Or was it the simple fact that anything tastes good after months of hardtack and salt pork?
At least in 19th century India, food became a major issue for British colonials. There was a widespread notion that the British constitution wasn't well-suited for spicy Indian food, and that it could make them physically ill. They often spent extra money to import "delicacies" such as hermetically-sealed salmon, red herrings, cheese, smoked sprats, raspberry jam, and dried fruits. They weren't just nostalgic for the food back at home - they felt that foreign food could actually damage their physical health and hybridize the colonial Briton, physically changing their bodies and altering their states of mind.
It's important to keep in mind that food is both material and intensely political. The way that people ate in foreign locales was tied up with issues of race and imperialism. E.M. Collingham has discussed this in Imperial Bodies and in Curry: A Tale of Cooks and Conquerors. She explains how eating Indian food - similarly to wearing Indian clothes or decorating the home with Indian art - was considered threatening to the maintenance of British-ness abroad. The British constitution was considered to be cold, but Indian cuisine was hot, and that could unsettle the balance of the body (according to 19th century logic). Especially after the Indian Rebellion of 1857, British officials felt that it was no longer safe in India, and they closed their bodies by eating only British food, wearing dark colors, and literally closing their estates to largely British residents.
Food is only one of many ways that culture and politics are embodied. I would certainly *not* say that food was simpler, and would argue that it was, in fact, incredibly complex. Especially when you consider the fact that, in India, British officials would sometimes eat preserved food from back in England rather than indulging in fresh food with spices that they enjoyed, and that later made their way into British cuisine. The Age of Sail is a really long time period, and it wasn't just a period of exploration, but one of imperialism and violence, and food played a significant role in that.
If you want to know more about food, the body, and power, I would recommend checking out Collingham's work. I should point out that she draws heavily on theories from Michel Foucault, Pierre Bourdieu, and Norbert Elias, and that this kind of interpretation is not without criticism from other historians of imperialism.
Edited for clarification.
The Spanish did not have that much of a hard time adapting to the new culinary realities of America in the early 16th century. Of course, being in a far away land with thigs entirely unfamiliar to you, you have to make do.
Some things gained immediate popularity, like chilis, being universally liked and praised by the likes of Gonzalo Fernández de Oviedo, Bernardino de Sahagún, José de Acosta and the whole lot. I commented on the chili/ají in this answer from a days ago.
If you go farther down the comments, you will find an article mentioning different animals that Oviedo ate and explained, including tortoises, jutías, alligators, etc. Among the animals the Spaniards ate in America, two gained a special prominence: iguanas and manatees. Manatees are praised for their meat, which Bartolomé de las Casas compares to tuna fish or similar other fish. Iguanas, being absolutely delicious, sparked a bit of controversy on whether they are land or water animals, and hence whether they are allowed to be eaten during Lent and periods of abstinence from meat. I commented on this issue a few days ago too.
Potatoes were praised by Pedro de Cieza de León, who mentions those plants to be similar to "turmas de tierra" (truffles), but potatoes did not quite catch on until much later in time. Francisco Cervantes de Salazar and Bartolomé de las Casas make the same comoarison. Cieza, however, brought some potatoes and planted them in his own orchard in Seville, for his own enjoyment (clever man and great writer he was).
Corn, and its derivatives like cazabí (corn tortillas or corn bread as mentioned in Spanish sources), on the other hand, caught on immediately, as it was the most immediately available cereal and it tastes great.
Edit: I absolutely forgot the tomatoes (shame on me), first brought to Europe by Cortés' fleet. From different sources it is easy to gather that they were a rapid success. Cervantes de Salazar mentions that they are great, and that people use them in America to make stews or sauces, especially the latter "in order to temper the heat of the ají [chili].