Is it safer for asthmatics to go visit the sea or the mountains?

Either: Depending on their particular allergies or triggers either or neither place might be safe. That being said, go and enjoy life and don't live in the grip of fear of the disease.

Depends on situation: If the asthma is well controlled either destination may be fine. However, if you live at lower altitudes & will transition quickly into a mountain area, it may bring out asthma issues & or make them more vulnerable to altitude sickness. One of my patients spent the week at denver children's while the siblings went skiing with their dad.