Depending on the country you aim to explore maintaining a vegan diet might be challenging. I experienced it to be a lot easier in asian countries because they use less animal products (especially milk products) in their traditional cuisine anyways.
What I learned to help a lot is to either bring oats with me or to buy oats within the first days of my journey. I can always ask for boiled water and a fresh fruit and that way prepare a healthy, vegan breakfast for myself (find out more about the health benefits of oats here). I experienced that in many countries they serve white bread and jam basically made out of sugar for breakfast and to me that’s not a proper breakfast.
Besides that I always try to buy nuts, seeds and fresh fruits on some markets and take them with me for long bus rides etc. I experienced that a lot of times they only offer chips and cookies during bus stops. I try to always make sure to have enough raw food while traveling because especially traveling can be challenging for the immune system and I want to provide my body with vitamines to stay healthy.I also ask locals how to say vegan in their language and then I add a detailed explanation in their language so I can use it while traveling. Especially when traveling in the countryside this is very helpful as people usually don’t even understand the concept (which is understandable). I save a recording of a local explaining it in their language as well as notes. That way I can always make myself understand easily.
Sometimes Im also a bit sad about not being able to explore the traditional dishes because they contain meat, but eating meat to me personally is disgusting. I just can’t even if I would wanted to. Thus I try to explore local fruits, vegetables and spices by going to markets. Sometimes I bring some traditional spices home and experiment with these new flavors. I have actually adapted some unusual spice combinations from my times abroad and love learning new ones every time I travel.