Are there any mistakes?

Some people prefer to travel abroad; others say there is much to be seen in our own country. Although both opinions make sense, I strongly believe that travelling abroad has more advantages.

To start with, visiting a foreign country enables us to learn about its culture and history and gives us the chance to observe how people there live and think. Besides, travelling abroad is an ideal opportunity to make friends with foreign people and learn their language. Last but not least, it is a chance to relax and do our favourite activities such as shopping and sightseeing.

To conclude, travelling abroad is fun and broadens the mind. It also teaches us to be more open-minded and more tolerant towards others.

What do you think of it? I'm supposed to give my opinion, so are the reasons given enough? Are there any mistakes? What is a sentence that can be used instead of 'both opinions make sense'? I want to say that both have advantages and that everyone has his own choice.

Really quite good! This sounds like a question from an FCE or IELTS test, so I think my only suggestion is to expand each reason: you made all three points in one single paragraph, when you could elaborate each point separately. New thought = new paragraph.

For a very short essay, it's perfectly fine.

As an alternative to "both opinions make sense" (this sounds like it came from a 'model' example), try something like "both perspectives are sound"... "sound" as in "healthy".